Developing and applying ICME + modeling tools to predict performance of additively manufactured aerospace parts

Developing and applying ICME 1 modeling tools to predict performance of additively manufactured aerospace parts

17

Brain W. Martin, Thomas K. Ales, Matthew R. Rolchigo and Peter C. Collins Department of Materials Science and Engineering, Iowa State University, Ames, IA, United States

17.1

Introduction

Integrated computational materials engineering (ICME) may be described as a generalized design framework that permits the prediction of relevant materials properties and performance of a given material and geometry subjected to a given set of boundary conditions that represents either a processing route or a lifetime of service. ICME integrates computational models and experimental data, often spanning across length and time scales. Successful ICME efforts permit engineering decisions to be made. Given that performance is comprised of statistical representations of individual properties, a perfect set of models is not required. Indeed, an “80% correct” set of models may provide a sufficiently accurate measure of performance to enable an engineering decision to be made (i.e., the goal of ICME efforts). The adoption of additive manufacturing (AM) into systems requires an approach for the informed qualification of processes and materials in an accelerated manner. ICME is an appropriate strategy to pursue to achieve such informed (and accelerated) qualification, as AM is a relatively new manufacturing approach, and does not have decades of historical data that is captured in a designers knowledge base. Notably, ICME frameworks can be quite individualized. The simulation tools and data that may be necessary for one ICME effort may not be necessary for another. Thus, what is presented in this chapter is an example of tools that may be integrated into an ICME framework for AM of metallic materials. To establish an ICME framework, it is necessary to understand the problem, and understand the key connections that require the integration of models and data. Thus, we first must consider the commonalities (and differences) between AM processes. AM may be generally described as any process that consists of the computercontrolled movement of a process zone in which new material is added volume-byvolume until a desired net- or near-net-shape part is produced. This definition (In principle, this definition can also accommodate emerging solid-state AM processes, Additive Manufacturing for the Aerospace Industry. DOI: https://doi.org/10.1016/B978-0-12-814062-8.00019-4 © 2019 Elsevier Inc. All rights reserved.

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although that is not the subject of this chapter.) is sufficiently broad, and easily accommodates all metal-based AM processes, which may have quite different energy (heat) sources (e.g., lasers, plasmas, or electron beams), environments (atmosphere, vacuums), and build rates. Fig. 17.1 provides a simple schematic showing the interaction between three primary variables associated with fusion-based AM processes. These three variables, along with the incoming feedstock (e.g., powder, wire) affect the physical processes during deposition. For example, a process that occurs under vacuum is likely selectively to lose certain alloying elements, depending upon their vaporization temperatures/partial pressures relative to those of other alloying elements. Alternatively, it is reasonable to expect that processes that occur under atmosphere would potentially getter trace interstitial elements (e.g., oxygen, nitrogen) from the inert atmosphere, depending upon the partial pressures and processing temperatures. The thermodynamics of the incoming material has a strong effect. For example, steel and aluminum can be processed under atmosphere or inert shield gases, whereas titanium requires high purity inert gasses or vacuum. Consequently, these changes in chemistry should be captured in an ICME framework for AM. Fig. 17.2 shows a proposed ICME framework for fusion-based AM processes, and Table 17.1 gives more details about the components that may be part of an integrated set of models to predict the fusion zone. It is important to note briefly that not all of the details, including specifically the thermophysical properties, are known for the temperature ranges relevant to these processes, as they often exhibit significant superheats.

Environment Possible not process

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Possible process

Possible process

Most AM processes

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tro

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a sm

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Figure 17.1 General schematic of different regimes of fusion-based AM processes. AM, Additive manufacturing.

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Probabilistic modeling (design allowables)

Integrated multiphysics fusion process model Energy–material–environment– interactions*

Input composition

Melting: Previous layer new material

Chemistry

Shape of molten pool

Melt pool physics (surface tension*, viscosity*, convection) State-of-matter interactions* (G–L, L–S, G–S) Heat-transfer

Solidification (GS, texture)

Physics-based property model Constitutive equations CP/FEM Defects S->S phase transf. microstructure Phase field Rules-based Data-based Part distortion Phase transformations

Figure 17.2 Linkages in a generalized ICME framework. ICME, Integrated computational materials engineering.  indicates aspects of a model which are themselves dependent upon the instantaneous condition of the simulated material state (e.g., temperature).

Given that the principal utility of an ICME framework is to enable an engineering decision to be made, it is clear that not every element of this proposed ICME framework is necessary for every problem. For example, if the primary objective of executing an ICME framework is to predict the residual stress of a component, it is possible to arrive at a reasonably accurate prediction by considering the heattransfer and macroscale thermal fields. However, if the primary objective is to predict the end composition (One of the challenges associated with the insertion of additively manufactured aerospace materials into applications is the fact that the composition changes during melt processes. Interstitial content will change, and for some processes and alloys, the fraction of primary alloying elements will also change (e.g., Ti
6Al
4V processed under vacuum can lose a large amount of its Al content due to preferential vaporization). Thus, the end fabricator may be responsible for certifying part composition.) of a component, other models are required in an ICME framework. For the purposes of this chapter, we will focus on a slightly simpler ICME framework, shown in Fig. 17.3. This framework informs the structure of this chapter. Assuming an input composition, we will first describe how certain physics of the process can be understood and modeled. These physics include: heat flow in both the melt pool and the whole part; fluid dynamics effects; and macroscale effects from uneven heating and cooling on the whole part. Once the process effects are understood and simulated, it is then possible to predict both chemistry and microstructure (influenced by both chemistry and the complex thermal history) within the final part, including an understanding of the nature of solidification and

Table 17.1 Selected details of aspects that might be included in a fusion process model General category of physics in the fusion zone

Details and examples

Energy
material interactions

Reflection, absorption, surface topographies where reflected energy at point X is absorbed at point Y, pressure/stress from income energy on liquid surfaces, ionization of elemental species in proximity to the interface Volatilization/absorption of certain elements and the attending changes in local stresses and temperatures at the liquid
environment interface when species leave/ absorb Scattering of incoming energy due to plumes and ionized material All of the physics of melting processes, including mass and thermal driven convection (Marangoni flow), melt pool shape, formation and collapse of keyholes, gravity, buoyancy, and the thermophysical properties that influence these processes (e.g., surface tension, viscosity, density) G
L: volatilization/absorption, details controlled by spatial distributions in elemental species and temperatures on both sides of interface, possible quantum effects. G
S: gaseous species “plating” of atomic species as they cool and potential solid-state absorption of interstitial elements such as oxygen and nitrogen when the solid is at a very high temperature. L
S: solidification/melting Primary heat flow modes (convection, conduction, radiation). Secondary heat flow modes due to surfacemediated processes, such as volatilization/absorption. Effects of heat flow on solidification and subsequent solid
solid phase transformations; part distortion; defect formation

Material
environment interactions

Energy
environment Interactions Melting

Interfacial Interactions between states of matter

Heat flow

Input composition

Process model

Chemistry model Physics-based property model Constitutive equations

Microstructure model Probabilistic modeling (design allowables)

Figure 17.3 Simplified ICME model that has been developed and applied for Ti
6Al
4V. ICME, Integrated computational materials engineering.

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reheating in AM builds. Once chemistry and microstructure are predicted, there have been models developed to predict properties, and subsequently performance, from microstructural and chemistry quantification as it varies within an AM part. We conclude by presenting some gaps in our current understanding, and thus our modeling capabilities.

17.2

Part 1: Process modeling

Our general understanding of the AM process, as it relates to final part properties, can be ascribed to two main regimes. The first relates to the overall thermal history of the final part, as well as uneven cooling rate and thermal histories resulting in residual stresses within the part. The complex localized thermal histories are also discussed, as a result of multiple reheats. This same regime, including the multiple reheats, is responsible for the solid-state phase transformations that lead to complex microstructures. The second regime includes the physics of the melt pool itself, which involves a complex multiphysical environment where heat flow (convection, conduction, and radiation) is coupled with fluid flow, mass transport, resulting in such complex phenomena as Marangoni convection and Plateau
Rayleigh instabilities that can lead to the formation of defects. The motion of the high-energy, highly localized heat source and relatively low heat conduction of some metals (including titanium, a critical alloy for aerospace components), results in large thermal gradients (G 5 |rT|) during the AM process. The motion of the highly localized heat source results in a complex thermal field that deviates from simple, Cartesian coordinate based thermal fields. Given that most AM processes involve multiple layers, with the heat source passing over previously solidified material, and it is clear that there is complex temporal nature to the thermal history. The theses of Kelly [1] and Ales [2] and the seminal works of the team of Denlinger, Martukanitz, and Michaleris [3
5] provide important modeling details to capture the thermal history of additively manufacturing, and some of the macrolevel effects (e.g., thermal cycling and thermal distortion). Due to expansion on heating and contraction on cooling, parts produced using AM often are affected by the creation of residual stress fields within each layer and across the entire part. While the exact nature and scale of these residual stresses depends on the part geometry, build rate, heat input, and thermophysical properties of the material, it is possible to draw some conclusions. For aerospace structural alloys, within each layer, cyclic expansion and contraction results in tensile stress at the top of the layer and compressive stress at the bottom. Collins et al. [6] compiled multiple modeling efforts to quantify the residual stresses present. The trend in terms of material type is higher stresses in Ni-based alloys (400
800 MPa), lower in Ti alloys (100
200 MPa), and even lower in Al alloys (25 MPa) [7]. Consistently, the tensile stresses within each layer were found to be greater than the corresponding compressive stresses. These macroscale residual stresses, which are fundamentally associated with gradients in strain-accommodating defects, such as

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dislocations, result in the large-scale distortion found in finished parts. One observation that has been made is that the size of the melt pool, which corresponds directly to the energy density of the build, was found to correspond directly with the residual stresses. A larger (and therefore hotter) melt pool resulting from slower build rates and/or a larger input power leads to higher thermal gradient. Experimental and modeling confirms that large thermal gradients result in higher residual stress. In one example, Martukanitz et al. [3,8] used data from in situ temperature measurements made during electron beam deposition of a 107 layer part. Data from the melt pool measurements were fed into a sophisticated thermal model, resulting in data that agrees with 3D scan distortion measurements (Fig. 17.4) [3]. In addition to the macroscopic distortion, the high levels of residual stress can result in cracking, layer delamination, or hot tearing either during or after deposition. There are at least two possible origins for these high residual stresses. First, the spatially varying cyclic thermal histories will result in local thermal distortion 60 Distortion (mm)

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5.00+01 0

Figure 17.4 (A) Experimental versus computational comparison of part distortion in a large AM build and (B) graphical representation of computational results [3]. AM, Additive manufacturing.

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due to the coefficients of thermal expansion. Second, for materials with solid
solid phase transformations, the repeated excursions through the solid phase transformations may lead to crystallographic strains that cannot be rapidly (and repeatedly) accommodated by the matrix crystal phases, resulting in the formation of defects. Interestingly, the formation of large residual stresses in a part may also have further effects on phase transformations not only in systems with strain-induced phase transformations (e.g., some types of martensites), but also in variant selection in alloys such as Ti
6Al
4V. For the purposes of the simplified example ICME outline shown in Fig. 17.3, we focus on the thermal history and its influence on the resulting chemistry and microstructure. As noted previously, other articles and theses deal very effectively with thermal modeling (e.g., [1
5,9
13]). Regarding the effects of the various physics of the molten pool and solidification, some very exciting modeling results have emerged over the past few years, and we present the generalities of this past research briefly. There has been a large body of work focused on the complex physics within the melt pool, especially in recent years [14
17]. Regarding these physics, the first consideration is the distribution of the heat within the molten pool, which is often (but not necessarily) modeled as a Gaussian distribution [18
20]. This ideal input distribution is likely rarely accurate, owing to scattering of incident photons or electrons by the vapor clouds and both “static” and dynamic powder in both powderblown and powder bed systems [15] (Fig. 17.5A). Further complicating these energy inputs is the fact that the absorptivity (often assumed to be an extrinsic variable) does change with surface temperature and surface topography, and is another physical factor that is considered in the modeling of this process. Knapp et al. [18] used a model to study the effect on the final part of the input power (see Fig. 17.5B), where the model included heat flow via radiation and conduction, mass input, fluid flow, and a moving heat source. In this work (and reassuringly), even excluding loss of mass via vaporization, the geometry of a single pass agrees with experimental results of nominally identical parameters, as seen in Fig. 17.5B. Another important physical process present in all AM systems is the Marangoni Effect. This is a mass flow fluid mechanics effect, where a gradient in surface temperature results in a force. In AM systems, this gradient in surface temperature is due to the presence of a steep thermal gradient. Often, the Marangoni Effect is responsible for the large amount of convection present in the melt pool and thus the primary means of ensuring chemical homogeneity in the melt pool. Models of powder bed fusion process have shown the effect of Marangoni convection on the geometry and motion within the melt pool [16] (see Fig. 17.5C). When the models are executed with a temperature independent, constant surface tension, a nonphysical bulbous melt pool is generated. While this melt pool shape can give some insight into the process [18], accounting for Marangoni allows the modelers to move closer to the reality. Others have demonstrated that accounting for the jet of metal vapor further changes the shape and motion of the pool. The study of this jet of vapor can lead to interesting insights as to otherwise unpredicted effects of the state of the build chamber environment. Matthews et al. [17] studied

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Homogeneous laser deposition

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60 80 100 120 140 160 180 200 220 240 60 80 100 120 140 160 180 200 220 240 60 80 100 120 140 160 180 200 220 240

Figure 17.5 (A) calculated absorptivity (a) for a bimodal powder bed, with the incident beam size given by the circles on the insets [15]; (B) calculated deposit shape, size, with information regarding temperature and fluid flow also provided immediately adjacent to transverse cross sections of as-deposited 316 L stainless steels at different powers (1500 W top and 2500 W bottom) [19]; (C) incremental inclusion of additional physics, showing the increase in model fidelity as heat transfer, melt pool depth, and fluid flow are all mediated by the additional physics that are noted in each sub-image [18].

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Figure 17.6 (A) Micrographs and (B) confocal height maps with varying argon pressure [17].

the effect of changing the argon pressure on a powder bed AM system, and found that this had a profound effect on the melt pool and powder available to be melted (Fig. 17.6). Larger positive argon pressure suppressed the negative pressure of the vapor jet and contributed to more metal powder being pulled into the melt track. As the argon pressure was taken to low values, the vapor jet was able to blow metal powder away from the melt track, and resulted in piled-up powder along the track. This vapor jet within the melt pool also leads to another important phenomenom in the AM process, which is the cyclic formation and collapse of a keyhole. With sufficient power input, the metal vapor within the melt pool can form a deep, narrow hole, which cyclically collapses and reforms, and can trap porosity in the build. This is most pronounced in the extremely high input power in electron beam processes, where the keyhole can even result in plasma jets that further complicate the process and any associated modeling effort [21,22]. Modeling of the keyhole has also been useful for predicting porosity in builds, with high speed camera imaging of the keyhole collapse and reform serving to verify the process models further, in both electron beam and laser systems [23]. Thus, porosity can result from both incomplete melting of the feedstock (i.e., when the energy density is too low, and insufficient for to achieve fusion) and the cyclic keyhole formation and collapse (i.e., which the energy is too high and causes elemental vaporization/volatilization). With respect to the subsequent solidification, generally speaking, solidification models can be ascribed to one of four main approaches: (1) process map models; (2) phase field models; (3) cellular automata models; and (4) kinetic Monte Carlo. The process map models typically start with concepts of heat transport and then

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60,000 Δt (0.0153 s) (A)

100,000 Δt (0.0255 s) (B)

135,000 Δt (0.0344 s) (C) 15

Model including fluid flow

10 20 µm

(D)

(E)

(F) 15

Control runs without fluid flow

0

Figure 17.7 Solute profiles in a Ti
xW system for models (A-C) including and (D-F) excluding fluid flow under different time steps in the model (real times in parentheses) [33].

calculate values of the thermal gradient (G) and the velocity of the solid
liquid interface (R), enabling the formulation of the so-called G
R plots that provide maps of the predominate types of microstructures based upon the operating solidification mechanisms. These approaches have been adopted for both titanium and nickel-based alloys [12,13,24
26]. Researchers pursuing phase field modeling for solidification have often coupled the phase field method with finite element modeling to calculate the macroscopic temperature fields [27,28]. Cellular automata has seen increased use (see an example showing the influence of calculated fluid flow in Fig. 17.7), as it is based upon a relatively simple framework where rules evolve over time, and can also capture some of the fundamental aspects of thermodynamics and diffusion [29
34]. The regular grid of cellular automata models is also beneficial, as it enables it to be linked with finite element methods that give the thermal gradients. Kinetic Monte Carlo [35,36] is the least well-explored method, but seems to show some promise for accurately predicting grain boundaries in multilayered AM builds.

17.3

Part 2: Predicting chemistry

The composition of structural alloys has a strong influence on not only the microstructure, but also directly on the mechanical properties through mechanisms such as solid-solution strengthening. Indeed, in previous work [37,38], it has been shown that the composition can be attributed to between 70% and 90% of the strength

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displayed by Ti
6Al
4V. As noted previously, the fact that fusion is the basis for current AM processes, it will be necessary to understand and predict chemistry of AM products. The final composition will likely be different from the starting composition, due either to interstitial pickup in atmosphere (including inert atmosphere) or solute loss due to preferential vaporization under vacuum. In addition to these macroscale effects, it is also necessary to consider the partitioning of solute species during solidification. Both composition effects will be considered below.

17.3.1 Solute loss (vaporization) or pickup (gettering) Previously, we have reviewed compositional variations found in many AM parts [6]. Since the AM process is a melting and solidification process, certification of the input material does not guarantee the final part will retain that chemistry. The presence of interstitial elements (e.g., oxygen, nitrogen, hydrogen) in the atmosphere, even in trace amounts (e.g., partial pressures in inert atmosphere), can have a pronounced effect on microstructure and mechanical properties. The use of metal powder feed, with its high surface-to-volume ratio, can exacerbate this problem as interstitial elements often lead to nanometer scaled surface layers, such as oxides or nitrides. Titanium, for example, is extremely susceptible to oxygen pickup, where oxygen serves to increase strength and lower ductility of titanium alloys. The mitigation of these effects can manage in the process environment, where a clean build chamber and careful control of the partial pressures of certain elements within the atmosphere can reduce any chemistry changes due to interstitial pickup. With regard to elemental loss during the process, it has already been established that the melt pool sees extremely high, localized temperatures. For AM techniques that occur under vacuum (e.g., electron-beam-based AM techniques), such high temperatures combine with the low pressures of the build environment and results in preferential vaporization of certain elements [6]. This evaporation of elemental species is related to the partial vapor pressure of the individual elements. The functional form of the partial vapor pressures is nonlinear with respect to temperature (e.g., in Ti
6Al
4V, Ales [2] has calculated the loss of Al under vacuum using the equation pAl(T) 5 10.917
16211/T, where the partial pressure is given in Bayres [39]). Elements with low vapor pressures and melting points relative to the other constituent elements are even more susceptible. While the problem is exacerbated for vacuum-based processes, similar vaporization does occur for all AM processes. One example is electron beam melted Ti
6
4, where aluminum levels can be reduced up to 15% by weight [40
42]. Laser systems, such as the Optomec LENS, have also seen reduction in Al content, and feedstock must be adjusted to compensate for this expected loss [43]. Thus, in addition to controlling the composition of the input material (i.e., powder, wire), it is also necessary carefully to control the temperature of the molten pool to achieve desired compositions of as-built parts. Often, the loss or pickup of elements throughout the AM process is simply reported with respect to the starting material, and few studies have tried to model the evaporation or condensation of elements. Given that AM is a nonequilibrium process, more complex modeling than simple partial pressure equations is needed.

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Semiatin [44] used the Langmuir equation to predict the flux at free surface of the melt (Js) for each element i, expressed as Js 5 Xi P0i γ i

rffiffiffiffiffiffiffiffiffiffiffiffi Mi 2πRT

where X is the mole fraction, P is the vapor pressure at absolute temperature T, γ is the activity coefficient for liquid melt, M is the molar mass, and R is the gas constant. Based on Semiatin’s approach, Collins [6] and Ales [2] have also applied the original Langmuir equation [45] to elemental absorption, where the mass flux towards the surface, m, is defined as rffiffiffiffiffiffiffiffiffiffiffiffi Mi m5 pi 2πRT where p is the partial pressure of element i. While the equations for interstitial flux seems to indicated that increasing temperature would lead to less interstitial pickup, increasing temperature means increasing melt pool size, and thus a greater area of flux for the elements, and conducted a simple analysis that shows this approach can be used to predict the gettering of interstitial elements from argon environments of varying purity. At the time of writing this chapter, the authors do note there are other issues that remain to be understood, including composition gradients adjacent to the molten pool. Thus, while there are quite possibly other factors at play, the rate of pickup and absorption of elemental species during the AM process is determined by surfacemediated flux. This also means that the melt pool itself is being sufficiently mixed as to be homogenous, and solute redistribution occurs primarily during solidification. The temperature and size of the melt pool is also an important parameter, and efforts should be made to monitor better and control the melt pool, so that the superheating of the melt pool is minimized [6].

17.3.2 Solidification partitioning The high cooling rates and high velocity of the solid
liquid interface in the AM process is consistent with definitions of rapid solidification. As this is a far-fromequilibrium process, there is the potential for significant supersaturation in the solid solution after the liquid-to-solid phase transformation. This can result in solute trapping within the final part, leading to distinctive features unique to the AM process. Aziz [46] presents a basis to understand the conditions under which solute trapping can occur, which can be rewritten for AM and is presented below, with respect to the velocity of the solidification front V, equivalent to the rate of solidification R. V 5R5

1 δT Dliquid c i jrTj δt a0

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Peak intensity of AI (a.u.)

60 (A)

(B)

55 50 45 40 35

0

50 100 150 200 250 300 Distance from top surface (µm)

Figure 17.8 Solute partitioning that leads to the so-called fish scaling and the subsequent local ordering (A) micrograph showing composition-driven fish-scaling and (B) composition profile across such bands [47].

In the above equation, T is the temperature, t is time, a0 is the interatomic spacing during growth, and Dliquid is the diffusion coefficient of solute in liquid. When this condition is satisfied, the liquid phase experiences solute trapping, and the solid solubility is extended. As the primary heat loss from the melt pool is via conduction into the as-built part, the highest thermal gradient is usually in the z-direction. This is directly related to the strong texture seen in AM parts, such as h0 0 1i fiber || z-direction. In addition to promoting a strong texture in AM parts, the high thermal gradient promotes solidification that initiates at the solid
liquid interface and proceeds along the maximum gradient. The solidification modeling activities, including the cellular automata models developed by Rolchigo [33,34] for various binary titanium alloys, show cellular structures with partitioning between the domains. The solidification also promotes other compositional partitioning, giving rise to features including the so-called fish scaling microstructural features [47] that correspond with geometric aspects of the molten pool, and which are visible in cross section. This solute trapping that can occur in additively manufactured metallic materials has various effects on microstructure and properties, including the formation of nonequilibrium phases. Tomus et al. [48] observed a supersaturation of the Al
2Sc system deposited with electron-beam AM process and noted that it corresponded with much higher properties than conventionally manufactured alloys. Thijs et al. [47] studied supersaturation and fish scaling in Ti
6Al
4V, and found some areas with Al content of up to 25 wt%, resulting in the formation of Ti3Al (Fig. 17.8).

17.4

Part 3: Predicting microstructure

As with any alloy system, chemistry strongly influences the microstructures of alloys produced using AM. However, given that one of the main benefits of AM is

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the ability to produce net- or near-net-shape components (i.e., no subsequent deformation processes to modify the microstructure), AM requires that the fundamentals of solidification be considered to engineer and control the microstructure. As noted previously, additively manufactured materials can exhibit a strong texture and spatial variation in the composition. One such alloy where texture exhibits a pronounced influence on the mechanical properties is Ti
6Al
4V. It has been shown that the texture can result in differences in the yield strength by at least 5% [38]. Ti
6Al
4V is one of the most widely used alloys, but is particularly susceptible to forming texture, given its very narrow freezing range. In principal, it should be possible to change chemistry and thus modify the texture by controlling the physics of nucleation and solidification. One such method is the growth restriction factor Q that was introduced by Maxwell et al. [49] and which has been used to describe the effect of solute concentration on the solidification and grain nucleation in cast alloys. Q is effectively a thermodynamic metric given as Q 5 mc0 ðk 2 1Þ 5

dΔTc dfs

where m is the slope of the liquidus line, k is the partition coefficient, and c0 is the solute concentration. In addition, the growth restriction factor is equivalent to the rate of development of constitutional undercooling (Tc) relative to the rate of development of solid (i.e., fraction solid fs). The grain refinement of cast titanium-based alloys with addition of boron was described, using this model, by Tamirisakandala et al. [50]. The observed effect of boron has also been exploited to refine grains and eliminate texture in β-Ti alloys by Mantri et al. [51]. Fig. 17.9 shows electron backscattered diffraction (EBSD) maps and pole figures of the four systems studied, where the addition of trace boron to binary Ti
V and Ti
Mo systems markedly decreased the grain size and eliminated the texture and large columnar grains. For the Ti
12Mo wt%, the addition of 0.5 wt% B resulted in a 100-fold reduction in grain size. In addition to the effects of the growth restriction factor, Mantri et al. attribute the insolubility of boron in titanium as having an effect where the rejection of boron to the solidification front resulted in a constitutionally supercooled front, and a larger frequency of grain nucleation. The effect of solute concentration, while a factor in some systems, does not always provide the full picture. A model was developed by Easton and St. John to describe, semiempirically, the effect of nucleant particles, combined with undercooling and the growth restriction factor, on the final average grain diameter in cast Mg and Al alloys [52,53]. The average grain diameter d is given as d5a1

b Q

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TD

1.733 1.553 1.391 1.246 1.116 1.000 0.896

RD

Figure 17.9 (A) EBSD maps and (B) the corresponding pole figures showing considerable grain refinement and reduction of peak textures of beta stabilized titanium alloys upon the incorporation of small amounts of boron [51].

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where a and b are defined in terms of the density of nucleant particles ρ, fraction of activated particles f, a constant b1, and the undercooling required for nucleation ΔTn: a5

1 ðρf Þ1=3

b 5 b1 ΔTn The Easton and St. John model proved useful for describing the effect of grain refinement of silicon on as-cast pure Ti [54]. Mendoza [19] applied the Easton and St. John model to explore the effects of tungsten on the grain refinement of binary titanium
tungsten alloys deposited using a powder-blown, laser-based AM platform. Fig. 17.10 shows the results of these studies, where increasing concentrations of W resulted in a measurable refinement in the resulting grains. While the singular effect of the growth restriction factor had a predominate effect on the grain refinement, the full Easton
St. John model was required to describe fully the effect by considering nucleation effects. Specifically, partially unmelted tungsten particles served as nucleation sites for grains during the rapid cooling of the AM process.

(A) (a)

Ti–5W

(b)

Ti–13W

10

15 % wt Tungsten

(c)

Ti–25W

100 µm

(B) 175 Grain size (µm)

150 125 100 75 50 25 5

20

25

Figure 17.10 (A) SEM micrographs and (B) stereo logically measured values showing the grain refinement of a binary Ti-xW system confirming the Easton-St. John model describing grain refinement during solidification [19].

Developing and applying ICME

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While these are just a few ways of controlling and modeling microstructure in AM parts via chemical additions, the application of older models developed for cast materials to new AM parts should continue to be explored. As with any new process, new alloy chemistries are needed fully to exploit the benefits of AM. Beyond these solidification microstructures, it is necessary to predict the solidstate phase transformations as well [3]. The types of modeling approaches that might be considered in predicting the solid-state phase transformations include: (1) classical methods, including the Johnson
Mehl
Avrami
Kolmogorov and Sestak and Berggren equations [55
65]; (2) the phase field method [66
69]; (3) and rules-based or database governed predictions that are based upon either modeling or experimental data.

17.5

Part 4: Predicting properties and performance

One of the main the goals of an ICME framework to understanding the AM process is to predict the mechanical properties, such as yield strength, toughness, or fatigue of a component based upon the previous elements in the ICME framework. We have previously accomplished this by rigorously quantifying [70] microstructural features, and using a hybrid modeling approach that integrated two machine learning tools, namely artificial neural networks (ANNs) with genetic algorithms (GAs) [37,38,41,71]. The ANN uses highly flexible functions (e.g., the hyperbolic tangent function) to establish the interrelationships that exist among a set of rigorously quantified input variables (e.g., composition, microstructure) and a set of output variables (e.g., yield strength, fracture toughness, fatigue [72
75]). Virtual experiments allow the trained ANNs to be explored in systematic ways. For example, by holding all of the input parameters except one at a single value, such as their average value for a given dataset, and then allowing that single input to vary over its range, it is possible to see the dependency of a property on that single input. This type of experiment is likely to be possible in a laboratory, given the complex and interdependent ways in which composition and microstructural features influence properties. The GA can then be exercised on the same dataset with a postulated equation where physically relevant terms are present. The GA then optimizes the equations, solving unknown weights and exponential powers, and once the equation is optimized, it can be compared to the ANN through the use of the same virtual experiments. The use of this approach has led to the deduction of a constitutive equation to predict strength of the material. A model that was previously developed for wrought structures was applied to additively manufactured Ti
6Al
4V. Over the course of our most recent work on large-scale AM of Ti
6Al
4V structures [38], we have made a few important discoveries. First, texture has a pronounced influence on the mechanical properties. Second, once texture is accounted for, the equation for wrought Ti
6Al
4V structures is nominally identical to additively manufactured Ti
6Al
4V. Third, the equations can be applied to any AM component, independent of subsequent heat

Predicted yield strength (MPa)

(A)

(B)

Yield strength-EBAM Ti-6AI–4v predicted vs experimental

1000 950

Pred. YS - α+β stress relief Pred. YS - α+β HIP Pred. YS - β anneal 0% +5% –5%

Fvα·89 + Fvβ·45+ 0.667 0.5 0.7 0.5 2 Fαv ·(149·xAI + 759·xo0.667) + Fvβ·((22·x0.7 v ) + (235·xFe ) ) +

900

σys =

850

–0.5 Fcol ·(tβ–nb)0.5+ v ·150·(tα–lath) –0.5 Fcol + v ·125·(tcolony)

800

(–1)·(AxisDebit) +

750

FBW v ·αMGb ρ

700 700 750 800 850 900 950 1000

Measured yield strength (MPa)

Probability

(C)

0.999 0.990 0.900 0.750 0.500 0.250 0.100 0.050

σYS, yield stress Phenomenological model Monte Carlo simulation

0.010 0.005

+/–σMSE +/–2σMSE

0.001 650

700

750

800

850 900 950 1000

Stress σ(MPa)

Figure 17.11 (A) Prediction of the properties of as-deposited Ti
6Al
4V subjected to three heat treatments [38]; (B) the equation corresponding equation [38]; and (C) a representation of a similar equation for the cumulative probability distribution of Ti
6Al
4V [76].

Developing and applying ICME

393

treatments, as long as the composition and microstructure can be measured or predicted accurately. Finally (and importantly), there is an unexpectedly large dislocation density in certain heat treatments (i.e., those that keep most of the as-deposited material state). The demonstration of a single equation to predict the strength of additively manufactured Ti
6Al
4V subjected to three different heat treatments is shown in Fig. 17.11A and B, with the predicted versus experimental data shown in Fig. 17.11A, and the equation presented in Fig. 17.11B, where the volume fractions of phases, size of features, and chemistry are included [38]. Continuing this demonstration of the ICME framework for additively manufactured Ti
6Al
4V, it is necessary to transition the prediction of properties to the prediction of performance. One way to interpret performance is through the use of cumulative probability distribution functions (pdfs), where the probability of achieving any given value of a property (e.g., yield strength) is plotted (see Fig. 17.11C; [76]). If the models described previously were to describe perfectly the properties of the material, the cumulative pdfs of the predicted data would overlap perfectly with experimentally measured data. However, even for good models, when looking at the data on a probability plot in which the tails of the data are emphasized, it may be that the model does not accurately predict the experimentally observed data. Thus, we have successfully turned to using a “distribution
translation
rotation” approach to shift and skew the models as necessary to represent the physical data. This statistical refinement of the model can occur in statistical space, and does not change the model. This approach has been previously reported in the literature [76], and additional publications will be forthcoming in the near future.

17.6

Limitations

Throughout the remainder of this chapter, we have referred to successful demonstrations of modeling activities, and/or have provided some important fundamental details to enable others to develop modules to an ICME approach. However, despite the successful outcomes that these activities have demonstrated, there are still limitations that need to be considered. Arguably, the most important limitations are associated with what we either do not know or have difficulty measuring/computing. Three limitations will be discussed briefly. The first limitation is associated with the fact that the process is quite complex, and multiple physics are active, potentially “erased” in the previous layer, and reactivated. In addition, many of the important physics associated with phase transformations, defect formation, chemistry, or texture formation occurs at different regions (e.g., solid-state phase transformations occur below the molten pool; nucleation events, convection, conduction, and instabilities occur within or at the surface of the molten pool; chemistry changes at the surface and above the molten pool; and solidification/solid-state phase transformations occur behind the molten pool) are characterized by details that are at either the nanosecond or nanometer scales. Currently, the AM community lacks the tools that may permit the investigation of

–60

3400 –100 (A)

(B)

(C) –55 –50

3300

–45

–80

–40

–60

–35

3200

–30 –25

–40

–20

3100

–15 –10

–20 3000

0

10

20

30

40

50

60

(D)

20 2900 40 2800

60 80

2700

100 –30 –20 –10 0 10 20 30

2600

Figure 17.12 (A) One direction SAW velocity map of electron-beam as-deposited Ti
6Al
4V; (B) the orientation map deduced from multiple SAW velocity maps; (C) the high resolution inset from (B); and (D) a tiled, mosaic optical image from the same region as (C). All units in (A) and (C) are in millimeters.

Developing and applying ICME

395

these physics at the appropriate length and time scales to understand what is happening. However, very recent investments in programs to develop in situ AM cells in synchrotron beamlines should allow the community to discover new science to understand better AM processes. The second limitation is associated exclusively with defects. In some systems, including titanium-based alloys, inspectability of additively manufactured components is a challenge. Spatial variation in the anisotropy of the as-deposited microstructures can interact with nondestructive evaluation techniques, providing new challenges when identifying defects, and potentially influencing the probability of detection (i.e., pod). The companion chapter in this volume speaks specifically to the challenges associated with nondestructive evaluation of additively manufactured articles. Interestingly, while there are challenges, the line-by-line, layer-by-layer of AM may permit the measurement of local microstructural state (including defects), and allow the so-called digital twins to be created for each component built. The third limitation that we will discuss briefly is the variation in scale of microstructural inhomogeneity. In traditional processing, the multistep forging sequences can chemically homogenize the material, and predictably produce texture that is relatively spatially consistent throughout a part. While texture can be controlled in AM [77], most AM processes have relatively small melt pools (e.g., ,1 mm). There are large-scale AM processes where the size of the molten pool permits heattransport mechanisms to compete and produce spatially varying microstructures, including texture (Fig. 17.12). As is apparent in the figure, the scales of these microstructural domains are much greater than what the materials scientist would typically measure. To measure the texture of these domains, the authors have turned to adopting a new technique (spatially resolved acoustic spectroscopy, or SRAS) to analyze the local orientation. During SRAS, a laser passes through a grating and sets up a surface acoustic wave (SAW), the velocity of which can be accurately determined. The velocity of the SAW is related to the elastic stiffness tensor (cij). If the SAW velocity and elastic stiffness tensor are known, the orientation can be calculated [78
81]. This method is especially exciting as it permits the measurement of texture and local orientation over areas that far exceed what is typically measured using other techniques. The limitation is the spatial resolution, which is currently B25 μm.

17.7

Summary

It is possible to develop and execute an ICME framework for structural metallic materials for aerospace applications. Any ICME framework is based upon a series of decisions that depend upon the overall objective. There are some exciting modeling activities that can be integrated into an ICME framework, including activities that predict distortion and solidification microstructures based upon a thermal history. One of the important aspects of any ICME framework is the ability to predict the composition of the as-deposited material, as it will invariably deviate from the

396

Additive Manufacturing for the Aerospace Industry

precursor powder or wire. The Langmuir equation has been used to predict elemental loss under vacuum and solute pickup under atmosphere. However, there are still unknown details of both the molten pool shape and the material transfer physics that will influence the successful implementation of the Langmuir (or similar) approach. Once chemistry is known, it is possible to couple chemistry with cooling rate and predict microstructure. Given a specific microstructure and composition, it is currently possible to predict the yield strength of the widely used aerospace alloy Ti
6Al
4V. Given the knowledge base that exists for certain aluminum-based alloys and nickel-based superalloys, it should be possible to integrate that knowledge into an ICME framework and make preliminary predications regarding their properties. Once a constitutive equation for properties is known, it is possible to predict the performance of the material, as represented by design allowables and the cumulative probability distribution function. While such modeling capabilities have been demonstrated, there are still gaps in the AM knowledge base. These gaps will be reflected in any ICME framework. However, there is extensive work underway to fill these knowledge gaps, and over the next decade, significant progress is expected.

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