JOM

DOI: 10.1007/s11837-014-1013-0  2014 The Minerals, Metals & Materials Society

Integrated Computational Materials Engineering of Titanium: Current Capabilities Being Developed Under the Metals Affordability Initiative M.G. GLAVICIC1 and V. VENKATESH2,3 1.—Rolls-Royce Corporation, Indianapolis, IN, USA. 2.—Pratt & Whitney, East Harford, CT, USA. 3.—e-mail: [email protected]

A technical review of the titanium model development programs currently funded under the Metals Affordability Initiative is presented. Progress of the ‘‘Advanced Titanium Alloy Microstructure and Mechanical Property Modeling’’ and ‘‘ICME of Microtexture Evolution and its Effect on Cold Dwell/High/ Low Cycle Fatigue Behavior of Dual Phase Titanium Alloys’’ will be reviewed followed by a discussion of the future modeling needs of the aerospace industry.

INTRODUCTION The aerospace industry uses titanium for a range of applications from fasteners to critical rotating hardware for turbine engines. There has been and continues to be considerable effort in the development of modeling and simulation tools that provide guidance for microstructure and mechanical property optimization. Much of the aerospace industry is interested in developing and using such computer-based simulation tools to develop next-generation components and processes with enhanced capabilities. This article provides a focused review on modeling and simulation of several key titanium features currently under development as part of two programs funded by the Metals Affordability Initiative (MAI). The intent of the format presented in the current article is to provide a broad overview of the titanium modeling efforts being worked within these two programs and to outline how these models are complementary. In order to do so, the article has been organized into two main sections, the first section titled, ‘‘Advanced Titanium Alloy Microstructure and Mechanical Property Modeling’’ and the second section, ‘‘ICME of Microtexture Evolution and its Effect on Cold Dwell/High/Low Cycle Fatigue Behavior of Dual Phase Titanium Alloys’’ even though the modeling results obtained in each of these two sections can be considered to be interdependent with one another.

ADVANCED TITANIUM ALLOY MICROSTRUCTURE AND MECHANICAL PROPERTY MODELING This project is a follow-on to two previously funded MAI programs that were aimed at developing and demonstrating titanium microstructure and mechanical property models on the most widely used titanium alloy, Ti64. In addition, under these programs, models were also developed to predict the crystallographic texture as a function of location in components using a post-processor-type linkage between the software package DEFORM (Scientific Forming Technologies Corporation, Columbus, OH) and the Los Alamos Polycrystalline Plasticity (LApp) code. These projects were extremely successful in developing tools to predict key microstructural features (primary alpha size and volume fraction, beta grain size, grain boundary alpha thickness, and lamellar alpha thickness) that could be used as inputs into a separate experimentally developed neural-network model that would predict the tensile properties and fracture toughness of specimens. In addition to these mechanical and microstructure properties, the ability to qualitatively predict the crystallographic texture was also demonstrated in this program.1 At the conclusion of these successful initial programs, one of the main deficiencies identified was the lack of unification of these modeling tools into a single user-friendly modeling tool that could be easily used in industry. This conclusion then led to

Glavicic and Venkatesh

Fig. 1. High-level overview of the ‘‘Advanced Titanium Alloy Microstructure and Mechanical Property Modeling’’ program.

the funding of the current MAI program (‘‘Advanced Titanium Alloy Microstructure and Mechanical Property Modeling’’) whose purpose is to further develop the tools developed under the previously funded programs into a unified software package for use in the aerospace industry. Moreover, the intent of the unified package of tools was to develop the ability to predict location-specific mechanical properties, crystallographic texture, and microstructure characteristics in wrought titanium alloy components. In order to unify the models under a single framework within an infrastructure commonly used in the aerospace industry, the commercially available finite-element software package DEFORM was selected as the main platform and was modified to use a series of plug-ins developed under this MAI program (Fig. 1). The changes made to DEFORM constituted both the inclusion of several new models within DEFORM as well as the addition of links to externally developed executable codes that are called by DEFORM at various stages during the modeling of forging and solution heat-treatment processes of titanium alloys. In the sections that follow, a brief description of the plug-ins developed in the order of how the modeling process works starting from the inputs and changes made to DEFORM is presented for duplex microstructure processed alloys only. The manner in which the beta-processed portion of the code operates is similar, but because of space restrictions its description is deferred to a later time. In general, the specific alloy chemistry of a billet inherently dictates the beta-transus temperature and beta-approach curve of the billet during heating. Because titanium alloy input stock is wrought and solution heat treated based on its beta-transus

temperature, DEFORM was first modified to read an ASCII input file that describes the beta approach curve of the specific billet stock material to be modeled. This beta approach curve may be generated either by hand or through the use of commercially available thermodynamic software packages. Under the current MAI program, modifications were made to the commercially available software package PanDat developed by CompuTherm LLC (Madison, WI) to generate a DEFORM compatible file automatically. In addition, DEFORM was also modified to read in a starting crystallographic texture for both the primary alpha and beta phases so that the crystallographic texture of the (I) primary alpha, (II) secondary alpha, (III) combined primary plus secondary alpha, and (IV) beta phases as a function of location in a forged and heat-treated component could be predicted. In order to make the package as flexible as possible, three input formats are accepted: (I) Los Alamos polycrystalline discrete orientation files using the Kocks Euler angle conventions, (II) electron backscatter diffraction files measured using the EDAX (TSL; EDAX Inc., Mahwah, NJ) software crystal conventions, and (III) electron backscatter diffraction files measured using the hkl software crystal conventions. The modeling of texture evolution within DEFORM during the hot working of two-phase, alpha/beta titanium alloys with a microstructure of equiaxed (primary) alpha in a matrix of beta is also complicated by several other factors that are also needed to be taken into account in the modifications made to DEFORM. First, the flow stress behaviors of the hexagonal-close-packed (hcp) alpha phase and the body-centered-cubic (bcc) beta phase differ and exhibit different dependences on temperature. Such

Integrated Computational Materials Engineering of Titanium: Current Capabilities Being Developed Under the Metals Affordability Initiative

differences result in an unequal partitioning of the imposed strain that drives the formation of deformation texture. Second, the beta phase decomposes to form secondary (platelet) alpha during cooling from the hot-working (or final heat treatment) temperature. At moderate cooling rates, this phase transformation follows a Burgers-type orientation relationship, f110gb ==ð0001Þa   10  h111i == 21 b

(1)

a

Suquet4 extended the above analysis to the case in which both phases are power-law viscoplastic, viz., i ri ¼ ki e_ m i

and the strain-rate sensitivity exponents for both phases are equal; i.e., m1 = m2 = m. In this case, the viscosity-like parameter of the aggregate (k) is a function of the values of viscosity-like parameters forthe two phases, k1 and k2, as well as m, q, and kLsc kL1 :

8 " #ð1  mÞ=2 9 < =     ðmþ1Þ=2 2 ð1  mÞ =  min kLSC L k=k1 ¼ f þ ð1  f Þqðm þ 1Þ=ðm  1Þ k2=k1 k 1 ; q  0:

in which 12 distinct possible variants can form from a single orientation of a prior beta-phase grain; i.e., the secondary-alpha orientation is related to one of six {110}b planes, each of which contains two h111ib directions. In addition, the transformation texture thus formed can vary widely depending upon the initial texture of the beta phase and any predisposition for one or several of the 12 variants to form preferentially over the others. In order to account for the variation of the flow stresses of the individual phases in alpha/beta titanium alloys such a function of temperature, DEFORM was modified to use a simple self-consistent approach2 that was previously developed. This method is based on the technique developed by Hill3 and later extended by Suquet4 for linearly elastic solids. Hill’s analysis assumed that both phases are linearly viscoplastic; i.e., they have a constitutive relation of the form: ri ¼

kLi e_ i

(2)

in which r and e_ denote the flow stress and strain rate, respectively; kL is the ‘‘viscosity’’ coefficient, and the subscripts (i = 1, 2) refer to phases 1 or 2. The viscosity of the aggregate kLsc (which relates the aggregate flow stress and strain rate) is given by the following expression: (  L L ksc k1 ¼ ð1=6Þ 3  2q þ 5ð1  f Þðq  1Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi) þ ½3  2q þ 5ð1  f Þðq  1Þ2 þ24q

ð3Þ

 in which q = kL2 kL1 , and f denotes the volume fraction of phase 1.

(4)

(5)

In Eq. 5, the expression on the right-hand side before the argument in braces denotes the minimum value for q ‡ 0. In practice, the value of kLsc =kL1 for the corresponding linearly viscous case is unknown. Thus, the evaluation of k/k1 involves a procedure in which trial values of q are guessed, kLsc =kL1 , is determined from Eq. 3, and q and kLsc =kL1 are inserted into Eq. 5. The value of q that yields the minimum value of k/k1 is the appropriate one. The average strain rates in the two phases are readily calculated from the values of k, k1, k2, and the volume fraction f of phase 1. Following Hill,5 the aggregate flow stress rov and strain rate e_ ov are volume averages of the corresponding flow stresses and strain rates in the individual phases: m m rov ¼k_em ov = fk1 e_ 1 þð1  f Þk2 e_ 2

(6)

e_ ov ¼ f e_ 1 þ ð1  f Þ_e2

(7)

Solving Eq. 7 for e_ 2 as a function of e_ ov and e_ 1 , e_ 2 =_eov ¼ ½1  f ðe_ 1 =_eov Þ=ð1  f Þ

(8)

Inserting this relation into Eq. 6, an expression for e_ 1 =_eov is obtained:  m h     m i ð1mÞ k2 k= ¼ f e_ 1= =k1 1  f e_ 1=e_ ov k1 e_ ov þ ð1  f Þ (9) Equation 9 cannot be solved analytically but is readily evaluated using numerical techniques. From Eqs. 8 and 9, the strain rates and hence strain increments for each phase are determined as a function of their relative flow stresses and volume fractions. The strain increments so determined were used in the crystal plasticity model that was incor-

Glavicic and Venkatesh

porated into DEFORM in order to estimate rotations due to slip. The manner in which a crystal plasticity model was incorporated into DEFORM was made as general as possible so that future upgrades would be permitted. In the current work, the crystal plasticity models previously developed at Cornell University were modified to model the texture evolution in the alpha and beta phases with the appropriate set arguments needed for compatibility with DEFORM. The code was then compiled into a dynamic link library and then linked to DEFORM. In order to allow the user to control the run time required to perform a forging simulation, two novel features were added to DEFORM and the Cornell University crystal plasticity code. The first feature enables the user to select how often the crystallographic texture is updated during a simulation as the updating of the local crystallographic texture in each of the elements from the imposed strains at all locations within the forging constitutes a heavy computation burden on the simulation time required. The second improvement allows the user to select the fidelity at which the local texture is represented through the selection of how coarse or fine the Rodrigues orientation space used to represent the texture is broken up. During cooling of a forging, at relatively slow cooling rates following hot forging (or heat treatment) of titanium components (i.e., <20C/min), primary alpha particles grow epitaxially, consuming the majority of the beta matrix.6 At faster cooling rates (between 20C/min and 200C/min), typical of fan cooling or water quenching of finitesection-size workpieces, the beta matrix decomposes at a critical supersaturation to form colonies of secondary-alpha platelets,7 each of which possess a Burgers-orientation relation with its parent beta matrix (Eq. 1). These two physical phenomena’s describe the upper and lower bound physics of what occurs during the processing of titanium alloys in the alpha–beta phase field over these aforementioned cooling rates. Furthermore, they describe the additional physics required and that needs to be incorporated within DEFORM in order to model the forging and heat treatment of titanium alloys in the alpha–beta phase field. In order to model the growth of the primary alpha phase and its ultimate volume fraction at ambient temperatures during cooling of a forging, the previously developed MEDC model8 was directly coded within DEFORM as an added feature within the software package. When used, the local cooling rate experienced at a given location in the forging is used to predict the local size and volume fraction of primary alpha present at that location. The thicknesses of the secondary alpha laths formed as a function of location are also derived from the local cooling rate experienced at a given location and is derived through the use of two new models developed under the current program. The

first model describes the temperature at which secondary alpha begins to form as a function of alloy chemistry, solution temperature, and local cooling rate. The second is a neural-network model that uses the local cooling rate at which secondary alpha nucleates in conjunction with the alloy chemistry and solution temperature to predict the thickness of secondary alpha laths formed at a given location. The texture associated with the secondary-alpha phase can vary greatly depending on which of the 12 possible variants is selected during beta-phase decomposition. The manner in which a beta phase orientation is transformed is governed by the relationship D Sbk B ¼ A

(10)

in which D is a rotation matrix, defined by the Euler angles u1 = 135, U = 90, u2 = 325,9 Sbk is a subset of the cubic symmetry operators (Table I), B is the beta phase orientation matrix, and A is the alpha phase orientation matrix. In the next set of modifications made to DEFORM three different variant-selection possibilities were examined. These rules were based on the previous experimental observations for commercial-purity titanium10–12 and Ti-6Al-4V.13–15 In the first case, all variants are assumed to be equally likely. In this instance, the modeled orientation distribution function that described the crystallographic texture of the beta phase is transformed into a crystallographic texture for the secondary alpha phase using all of the rotation matrices Sbk from Table I. In the second case, the generalized Schmid factors for restricted slip on the {110}h111i slip systems in the beta phase as a function of the imposed thermal stresses were examined to determine which variant was preferentially formed. Specifically, the local stress states were calculated at each location in the forging. The {110}h111i slip system on which the highest resolved shear stress had been developed was assumed to comprise the plane/direction that determined the orientation of the selected alpha variant. Because the variants of the alpha phase are assumed to form per the Burgers relationship (Eq. 1), the resolved shear stress s on a given {110}h111i slip system in the beta phase for a given imposed stress state will be the same as the 10  slip system in resolved shear stress on the ð0001Þ½21 the alpha phase after the phase transformation. The equivalent slip planes/directions of the beta and alpha phase are then related by ðsÞ

hai : ArAT s ¼ mb : BrBT ¼ mbasal a basalhai

(11)

in which hm(s) are the tensor quantities b and mai ðsÞ 1 ^ ^ mij ¼ =2 bi n^j þ bj n^i , in which the slip direction b^ and slip plane normal n^ are defined by {110}h111i 10  slip systems of the beta phase and the ð0001Þ½21 slip system of the alpha phase. Inserting Eq. 10 into Eq. 11

Integrated Computational Materials Engineering of Titanium: Current Capabilities Being Developed Under the Metals Affordability Initiative Table I. Subset of cubic symmetry operators used to transform the beta phase into distinct alpha phase variants 2 3 2 3 2 3 1 0 0 0 1 0 0 0 1 b b b S5 ¼ 4 0 0 1 5 S9 ¼ 4 1 0 0 5 S1 ¼ 4 0 1 0 5 0 0 1 1 0 0 0 1 0 2 3 2 3 2 3 0 0 1 0 1 0 1 0 0 Sb2 ¼ 4 1 0 0 5 Sb6 ¼ 4 0 0 1 5 Sb10 ¼ 4 0 1 0 5 0 1 0 1 0 0 0 0 1 2 3 2 3 2 3 0 1 0 0 0 1 1 0 0 b b b S7 ¼ 4 1 0 S11 ¼ 4 0 1 0 5 S3 ¼ 4 0 0 1 5 0 5 1 0 0 0 1 0 0 0 1 2 3 2 3 2 3 0 1 0 0 0 1 1 0 0 0 15 Sb8 ¼ 4 1 0 0 5 Sb12 ¼ 4 0 1 0 5 Sb4 ¼ 4 0 1 0 0 0 1 0 0 0 1

(a)

16 14 10 8 6 4 2

3.6

(b)

(100)

(110)

2.9

(111)

2.5 2.1

TD

1.7 1.3 1.0

Fig. 3. Contour plot of the volume fraction of primary alpha as a function of location within the double-cone compression specimen.

0.6

RD

Fig. 2. Location-specific crystallographic texture within the double cone compression specimen examined: (a) orientation distribution function and (b) pole figures of the beta phase.

 T ðsÞ b b hai mb : BrBT ¼ mbasal : DS Br DS B a k k

(12)

permits the specific alpha phase variant DSbkB that has the same resolved shear stress as in the beta phase to be selected from the 12 possible variants and used to transform the beta phase orientation. In the third case, variants whose Kearns numbers most closely match the Kearns numbers of the primary alpha phase are selected preferentially from the 12 possible orientations. Depending upon the localized cooling rate experienced in the forging, any of these three cooling rates may be used that best represents the crystallographic texture of the secondary alpha phase formed. Having determined the location specific microstructure (primary alpha size, volume fraction, and

secondary alpha lath thickness) and crystallographic texture of all phases (primary alpha, secondary alpha, combined primary plus secondary, and beta), a second novel neural net is then used to predict the location-specific mechanical properties (yield strength, ultimate tensile strength, percent elongation, and reduction of area). Finally, in order to extract model results at a specific locations and view the variability of the location specific microstructures, properties, and texture developed, DEFORM was updated with the ability to display all of these new attributes within the DEFORM post processor. In order to provide the reader with a view of the new capabilities developed under this program, a simulation using a double cone specimen with nonproprietary boundary conditions imposed was completed. Following a forging simulation, the textures of any of the phases (primary alpha, secondary alpha, and combined primary plus secondary alpha and beta phase) at any given location may be displayed

Glavicic and Venkatesh

Fig. 4. Contour plot of the particle size of primary alpha as a function of location within the double-cone compression specimen.

Fig. 6. Contour plots of predicted mechanical properties (a) yield strength (YS) and (b) percent reduction in area (RA%) as a function of location. Fig. 5. Contour plot of the secondary alpha lath thickness as a function of location within the double-cone compression specimen.

in the form of either an orientation distribution function or in the conventional pole figure format (Fig. 2). Moreover, contour plots of the volume fraction of primary alpha (Fig. 3), primary alpha size (Fig. 4), and secondary alpha lath thickness (Fig. 5) may also be viewed within the GUIs developed. Finally, the tensile properties such as yield strength, ultimate strength, percent elongation, and reduction of area, at any given location, may be determined and tabulated within the GUIs (Fig. 6) developed so that the mechanical anisotropy in a forged component may be inspected and taken into account during component design. ICME OF MICROTEXTURE EVOLUTION AND ITS EFFECT ON COLD DWELL/HIGHCYCLE/LOW-CYCLE FATIGUE BEHAVIOR OF DUAL-PHASE TITANIUM ALLOYS The objectives of this MAI program are to develop: (I) processing routes to reduce microtextured

regions (MTRs) in two most widely used titanium alloys, Ti-64 and Ti-6242, (II) improved methods to quantify MTR using electron backscatter diffraction (EBSD) and ultrasonic testing (UT) techniques in titanium billet and forgings, and (III) integrated computational materials engineering (ICME) aimed at developing and integrating process and property modeling tools for the prediction of microtexture and fatigue life in titanium components. Benefits from the tools and methods developed in this program will stem from: (I) reduced development and qualification cost and cycle time for future components; (II) enhanced process optimization for existing components leading to reduction in scrap, rework, and excessive quality control testing; and (III) increased performance of components through microstructure and mechanical property prediction tools leading to reduced scatter and the use of lower cost alloys. The impact of this project will benefit the entire aerospace supply chain, including raw material suppliers, component suppliers, and original equipment manufacturers (OEMs). An activity integrated project team (AIPT) comprising of titanium billet producers (RTI and PCC-

Integrated Computational Materials Engineering of Titanium: Current Capabilities Being Developed Under the Metals Affordability Initiative

Fig. 7. BSE images taken at the midradial locations of (a) good process and (b) bad process billets.

TIMET), forging suppliers (ATI-Ladish and PCCWymon Gordon), OEMs (Pratt & Whitney, Rolls Royce, GE, and Boeing), characterization specialists (Materials Resources LLC and The Ohio State University), modeling specialist (DEFORM), and The U.S. Air Force Research Laboratory was formed to work on this project. The first task in this program was to understand the link between key ingot to billet conversion process variables and microtexture in dual-phase titanium alloys.16,17 In order to accomplish this task, the AIPT ranked process variables that are likely to have a high impact on microtexture in billet and final forged components. Highly ranked process variables included the path and magnitude of strain components, temperatures, transfer times and cooling rates from the beta processing stage. It should be noted that a number of these parameters are intrinsically controlled by the geometrical characteristics; e.g., total strain levels are controlled by start and finish size and shape of billet, as is the cooling rate by the beta quench billet shape and size. The previously identified process variables were used to manufacture two subscale Ti-6242 billets, with different levels of microtexture. One billet was expected to exhibit low levels of microtexture, referred to as ‘‘good’’ process billet, and the other is expected to deliver higher levels of microtexture, referred to as ‘‘bad’’ process billet. The team judicially designed the process such that it will be upscalable to produce full-scale billets with controlled levels of microtexture. Characterization of the microtexture and microstructure at the various locations and stages of processing was performed using EBSD and backscattered electron (BSE) imaging techniques. The microstructure of samples taken from the ‘‘good’’ and ‘‘bad’’ billets at the end of the beta processing stage revealed alpha colonies in large prior beta grains decorated by alpha along the grain bound-

aries (Fig. 7). The average colony lath and boundary alpha width was observed to be much finer in the ‘‘good’’ process billet. The microstructure of the two subscale billets showed a higher degree of alpha spheroidization along with finer alpha grains in the good billet than the bad billet, which exhibited coarse alpha features with a lower level of alpha spheroidization (Fig. 8). The EBSD scans collected for the good and bad billets from the center, midradius, and edge locations of the finished billets revealed microtextured regions with different morphologies. MTRs in the ‘‘bad’’ process billet were generally elongated along the billet longitudinal axis but were much shorter in length and thicker than MTRs in the ‘‘good’’ process billet, which are thinner and extend to nearly the full length of the scan (Fig. 9). The size of each scan was 8 mm 9 8 mm with a 5-lm step collected as 500-lm square tiles, giving 2.56 9 106 EBSD points per scan over 256 tiles. In order to evaluate the evolution of microtexture from billet to final forged components, a total of 18 specimens were extracted from ‘‘good’’ and ‘‘bad’’ process billets and were isothermally compressed at two alpha–beta temperatures (1680F and 1750F) and two strain rates (0.1 s1 and 1.0 s1). Compression samples exhibited deformed MTRs associated with the nonuniform strain gradients experienced in the specimen. As an example, Fig. 10 shows inverse pole figure (IPF) maps from the three scan locations for ‘‘good’’ billet sample compressed at 1750F and 0.1 s1. Large-area EBSD data from both billet and compression samples were used to identify and quantify the microtextured zones. Specifically, MTRs were identified by clustering data points by crystal orientation and spatial location, followed by segmenting the identified regions into classes of common orientation and measuring chord length distributions for each segmented class. Following identification and classification of MTRs, quantification

Glavicic and Venkatesh

Fig. 8. BSE images of the (a) good-processed billet and (b) bad-processed billet at the midradial location. The billet longitudinal axis is oriented vertically.

Fig. 9. Inverse pole figure map of (a) ‘‘good’’ billet center location, and (b) ‘‘bad’’ billet center location. The billet longitudinal direction is oriented vertically.

Fig. 10. IPF maps from the edge (left), midradius (center), and center (right) locations of Ti-6242 ‘‘good’’ billet sample compressed at 1750F and 0.1 s1. The compression axis is oriented vertically along the original billet longitudinal axis.

Integrated Computational Materials Engineering of Titanium: Current Capabilities Being Developed Under the Metals Affordability Initiative

(a)

(b)

3

3

Center

2

2

1

1

0

0

-1

-1

-2

-2

-3 -6 Good Class 1 Class 2 Class 3

-4

-2

0

2

Mid-Radial

-3 -6

4

-4

-2

0

4

Bad Class 1 Class 2 Class 3

Good Class 1 Class 2 Class 3

Bad Class 1 Class 2 Class 3

2

(c) 3

Edge

2 1 0 -1 -2 -3 -6

-4

Good Class 1 Class 2 Class 3

-2

0

2

4

Bad Class 1 Class 2 Class 3

Fig. 11. PCA of mean and mode of length and width data for three classes of microtextured zones: (a) center, (b) midradial, and (c) edge. Plots show that MTRs for good and bad material have distinctly different characteristics.

using the two-point statistics of each class was conducted to extract average width and length of each MTR.18 The average MTR length-to-width ratio in the ‘‘good’’ billet ranged between 1.21 and 1.32, whereas for the ‘‘bad’’ billet the ratio ranged from 1.76 to 2.21. Principal component analysis (PCA), which is a statistical procedure that transforms a larger set of correlated variables into a smaller set of variables called principal components, was applied to the mean and mode values of the MTR metrics.19 The results, shown in Fig. 11, revealed clear differences between the good and bad processed MTRs at three billet locations. PCA was very effective in this case to explore the cogging process variables to generate predictor combinations that influence good and bad MTR metrics (Fig. 11). DEFORM finite-element analysis was carried out from the billet cogging stages to the completion of isothermal compression tests. Location-based data sets of strain, strain rate, and temperature compo-

Fig. 12. Neural-network model using the Pattern Master software trained on effective strain, strain rate, temperature, and starting billet major and minor MTR axis to predict final major and minor MTR axis in compressed samples.

nents were extracted to determine the key state variables that influence the evolution of microtexture from billet to final compressed samples. Final compressed strain, strain rate, and temperature variables on location basis, together with starting

Glavicic and Venkatesh

orthogonal sides of samples prepared for microtexture characterization from the ‘‘good’’ and ‘‘bad’’ process billets and for isothermally compressed samples. Raw ultrasonic data were processed to obtain ultrasonic backscattering and attenuation maps. A further analysis using inverse ultrasonic models, developed at The Ohio State University, provides the average morphology and size of microtextured regions.20–23 An analysis of ultrasonic results from ‘‘good’’ and ‘‘bad’’ billet samples at the beta processed stage showed that the microstructure, consisting of beta grains and transformed alpha colonies, is relatively equiaxed. In contrast, results from subscale billets indicated the presence of nonequiaxed, microtextured regions. The results revealed that the average length-to-width ratios for MTRs in the subscale billets range from 3 to 6.5. Four longitudinally compressed samples that were characterized exhibited on average nearly equiaxed MTRs, which match closely with EBSD metrics. SUMMARY All the microstructure and property modeling tools described herein will be linked into DEFORM by SFTC at the end of these programs. These models will be used to design new production-scale practices to manufacture Ti-6-4 and Ti-6-2-4-2 components with optimal microstructure and microtexture. Application of the technology developed under these programs could be used in the design of new lower weight components with higher buy-to-fly ratios in which their properties, as a function of location, are used in the overall component design. Successful completion of these projects will represent a major advancement in the industry, as the industry seeks to implement innovative technologies that will allow the supply base to provide critical turbine engine and airframe components that meet U.S. military and commercial aerospace requirements. ACKNOWLEDGEMENTS Fig. 13. Neural-network model predictions for training and validation data sets showing correlation with EBSD measurements of (a) length MTR dimensions and (b) width MTR dimensions in lm.

billet MTR dimensions, were used to train a neuralnetwork model (Fig. 12). A total of six compression conditions from the ‘‘good’’ billet and seven from the ‘‘bad’’ billet were used to train the Pattern Master neural network, and five remaining sample conditions were used as testing sets to evaluate the capability of the neural-network model to predict final MTR metrics (Fig. 13). The neural network was able to generalize the trends between the input and output variables and to provide good predictions of length and width MTR dimensions for the validation data sets. Nondestructive ultrasonic characterization of Ti-6242 samples extracted from billets and small compression samples was also performed in this program. Ultrasonic imaging was conducted on the

The authors would like to acknowledge the support of the U.S. Air Force through the Metal Affordability Initiative (contracts FA8650-10-2-5219 and FA8650-13-2-5203) and the following team members: A. Pilchak, S.L. Semiatin, and C. Woodward from AFRL; T. Morton from Boeing; T. Broderick from GE; A. Salem from MRL; S. Rokhlin from The Ohio State University; Y. Kosaka, and K. Calvert from TIMET; S. Tamirisa, and J. Sartkulvanich from RTI; V. Saraf from ATI, P. Kumar from WG-PCC; I. Cernatescu from P&W; F. Zhang from Computherm; D. Boyce From Cornell University; and R. Shankar, W, Wu, and J. Zhang from SFTC. REFERENCES 1. D. Furrer, A. Chaterjee, G. Shen, A. Woodfield, S.L. Semiatin, J. Miller, M. Glavicic, R. Goetz, and D. Barker, Proceedings of the 11th International Confernce on Titanium, ed. M. Ninomi (Sendai, Japan: JIM, 2007). 2. S.L. Semiatin, F. Montheillet, G. Shen, and J.J. Jonas, Metall. Mater. Trans. A 33A, 2719 (2002).

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