Predicting the tensile properties of additively manufactured Ti-6Al-4V via electron beam deposition

Additively manufactured materials are gaining wide attention owing to the manufacturing benefits as it results in near net shape components. It is well known that the manufacturing processes affects the performance of the components via microstructural features and the mechanical properties. There is an urgent need to understand the processing-structure-property-performance relationship for the materials manufactures via such innovative techniques. Strategies are needed to quantify and modify the mechanical properties. This study assists to design and tailor the process parameters based on the final properties required. Current work predicts the yield strength of additively manufactured Ti-6Al-4V with different post heat treatments. A thermal model predicted by ABAQUS is fed into an implementation of Langmuir equation that predicts the chemistry which is then used in a phenomenological equation predicting the yield strength. The model is confirmed via experiments showing less than 2% deviation from the predicated properties. A statistical model gives design allowables that have an uncertainty of less than 1 ksi. Disciplines Manufacturing | Materials Science and Engineering Comments This proceeding is published as Ales, Thomas, Iman Ghamarian, Brian Hayes, Brian Welk, Andrew Baker, Matthew Kenney, D. Gary Harlow, Hamish Fraser, Wenqi Li, and Peter Collins. "Predicting the tensile properties of additively manufactured Ti-6Al-4V via electron beam deposition." MATEC Web of Conferences 321 (2020): 11083. DOI: 10.1051/matecconf/202032111083. Posted with permission. Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 License. Authors Thomas K. Ales, Iman Ghamarian, Brian Hayes, Brian Welk, Andrew Baker, Matthew Kenney, D. Gary Harlow, Hamish Fraser, Wenqi Li, and Peter C. Collins This conference proceeding is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/ mse_conf/49 Predic ng the tensile proper es of addi vely manufactured Ti-6Al-4V via electron beam deposi on Thomas Ales1, Iman Ghamarian1, Brian Hayes1, Brian Welk2, Andrew Baker3, Ma�hew Kenney1, D Gary Harlow4, Hamish Fraser2, Wenqi Li5, Peter Collins*,1 1: Iowa State University, Ames, IA, United States 2: Ohio State University, Columbus, OH, United States 3: The Boeing Company, St. Louis, MO, United States 4: Lehigh University, Bethlehem, PA, United States 5: University of No ngham, No ngham, United Kingdom Abstract Addi vely manufactured materials are gaining wide a�en on owing to the manufacturing benefits as it results in near net shape components. It is well known that the manufacturing processes affects the performance of the components via microstructural features and the mechanical proper es. There is an urgent need to understand the processing-structure-property-performance rela onship for the materials manufactures via such innova ve techniques. Strategies are needed to quan fy and modify the mechanical proper es. This study assists to design and tailor the process parameters based on the final proper es required. Current work predicts the yield strength of addi vely manufactured Ti-6Al-4V with different post heat treatments. A thermal model predicted by ABAQUS is fed into an implementa on of Langmuir equa on that predicts the chemistry which is then used in a phenomenological equa on predic ng the yield strength. The model is confirmed via experiments showing less than 2% devia on from the predicated proper es. A sta s cal model gives design allowables that have an uncertainty of less than 1 ksi.Addi vely manufactured materials are gaining wide a�en on owing to the manufacturing benefits as it results in near net shape components. It is well known that the manufacturing processes affects the performance of the components via microstructural features and the mechanical proper es. There is an urgent need to understand the processing-structure-property-performance rela onship for the materials manufactures via such innova ve techniques. Strategies are needed to quan fy and modify the mechanical proper es. This study assists to design and tailor the process parameters based on the final proper es required. Current work predicts the yield strength of addi vely manufactured Ti-6Al-4V with different post heat treatments. A thermal model predicted by ABAQUS is fed into an implementa on of Langmuir equa on that predicts the chemistry which is then used in a phenomenological equa on predic ng the yield strength. The model is confirmed via experiments showing less than 2% devia on from the predicated proper es. A sta s cal model gives design allowables that have an uncertainty of less than 1 ksi. 1. Introduc on In the main, it is desirable to have an integrated computa onal materials engineering (ICME) strategy to predict the proper es of addi vely manufactured materials, and thereby accelerate the applica on of these advanced manufacturing approaches by various commercial companies. In any ICME strategy, it is necessary to fully understand and capture the relevant details of the materials science paradigm: composi on, processing, microstructure, proper es, and performance. This work represents a mul -ins tu on, 6-year effort to develop a robust ICME strategy capable of predic ng the proper es and performance of addi vely manufactured Ti-6Al-4V to within 7MPa (1ksi). Key components of the framework include: (i) a thermal model; (ii) a Langmuir-based model to predict the asdeposited composi on; (iii) a phase field model to predict the microstructure; (iv) an ar ficial neural network-gene c algorithm extracted phenomenological equa on to predict strength; (v) a sta s cally based model for the probabilis c predic on of strength; and (vi) an ABAQUS model and framework that integrates the knowledge of the program into a predic ve tool. 2. Materials and Experiments MATEC Web of Conferences 321, 11083 (2020) https://doi.org/10.1051/matecconf/202032111083 The 14 World Conference on Titanium © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). To develop an ICME framework, a large-scale method of addi ve manufacturing (i.e., the Sciaky electron beam addi vely manufactured (EBAM) process) was selected to produce Ti-6Al-4V. This par cular method uses a high energy electron beam as a heat source, which operates under vacuum, and feeds in a wire that is melted and added to the previously deposited material. The as-deposited material was sec oned and subjected to various thermal histories [1]. The sta c mechanical proper es were determined, and a database was developed that consisted of measurements of the as-deposited composi on, microstructure, and mechanical proper es. A variety of state-of-the-art materials characteriza on techniques were adopted, ranging from the more rou ne backsca�ered electron microscope images that were subsequently quan fied to advanced precession electron diffrac on techniques that were applied to spa ally resolve and quan fy disloca on densi es by rela ng the presence of such defects to la ce curvature at a nm length scale [2]. Following materials characteriza on, a physically based equa on was developed using a hybrid ar ficial neural network gene c algorithm approach that has been described elsewhere. Briefly, this approach permits a gene c algorithm approach to match an n-variable equa on that has been determined using the flexible ar ficial neural network to a n-variable phenomenological equa on that has been postulated based upon known physics. The resul ng equa on overcomes several of the limita ons of ar ficial neural networks, including devia ons in the equa on in regions of data sparsity. This equa on, originally developed for wrought Ti-6Al-4V, was modified slightly for the addi vely manufactured material. Specifically, a texture debit term was introduced for the observed decrease in yield strength along the primary x-y-z cartesian coordinate axis, and a Taylor hardening terms incorporated for varia ons in disloca on density. A sophis cated sta s cal approach was incorporated to manage the small variability that exists between the predicted values and the experimentally measured values when both simulated and experimentally measured data is plo�ed on a cumula ve probability distribu on func on plot (c-pdf). A sta s cal adjustment of the model data and experimental data is sufficient to apply to future data and have such future data lie almost perfectly on the c-pdf. In parallel, an ABAQUS code was developed to predict: the thermal history; the chemistry varia on due to vola liza on of certain species under vacuum; the microstructure; and the resul ng sta c mechanical proper es. The predicted c-pdfs were compared to the measured c-pdfs and found to be in very good agreement. 3. Results and Discussion The results of this work are extensive, and too broad to appear in this proceedings paper. For complete descrip ons, the reader is pointed elsewhere [3-6]. The most important details of this work are given below.


Abstract
Addi vely manufactured materials are gaining wide a�en on owing to the manufacturing benefits as it results in near net shape components. It is well known that the manufacturing processes affects the performance of the components via microstructural features and the mechanical proper es. There is an urgent need to understand the processing-structure-property-performance rela onship for the materials manufactures via such innova ve techniques. Strategies are needed to quan fy and modify the mechanical proper es. This study assists to design and tailor the process parameters based on the final proper es required. Current work predicts the yield strength of addi vely manufactured Ti-6Al-4V with different post heat treatments. A thermal model predicted by ABAQUS is fed into an implementa on of Langmuir equa on that predicts the chemistry which is then used in a phenomenological equa on predic ng the yield strength. The model is confirmed via experiments showing less than 2% devia on from the predicated proper es. A sta s cal model gives design allowables that have an uncertainty of less than 1 ksi.

Introduc on
In the main, it is desirable to have an integrated computa onal materials engineering (ICME) strategy to predict the proper es of addi vely manufactured materials, and thereby accelerate the applica on of these advanced manufacturing approaches by various commercial companies. In any ICME strategy, it is necessary to fully understand and capture the relevant details of the materials science paradigm: composi on, processing, microstructure, proper es, and performance.
This work represents a mul -ins tu on, 6-year effort to develop a robust ICME strategy capable of predic ng the proper es and performance of addi vely manufactured Ti-6Al-4V to within 7MPa (1ksi). Key components of the framework include: (i) a thermal model; (ii) a Langmuir-based model to predict the asdeposited composi on; (iii) a phase field model to predict the microstructure; (iv) an ar ficial neural network-gene c algorithm extracted phenomenological equa on to predict strength; (v) a sta s cally based model for the probabilis c predic on of strength; and (vi) an ABAQUS model and framework that integrates the knowledge of the program into a predic ve tool.

Materials and Experiments
To develop an ICME framework, a large-scale method of addi ve manufacturing (i.e., the Sciaky electron beam addi vely manufactured (EBAM) process) was selected to produce Ti-6Al-4V. This par cular method uses a high energy electron beam as a heat source, which operates under vacuum, and feeds in a wire that is melted and added to the previously deposited material. The as-deposited material was sec oned and subjected to various thermal histories [1]. The sta c mechanical proper es were determined, and a database was developed that consisted of measurements of the as-deposited composi on, microstructure, and mechanical proper es. A variety of state-of-the-art materials characteriza on techniques were adopted, ranging from the more rou ne backsca�ered electron microscope images that were subsequently quan fied to advanced precession electron diffrac on techniques that were applied to spa ally resolve and quan fy disloca on densi es by rela ng the presence of such defects to la ce curvature at a nm length scale [2].
Following materials characteriza on, a physically based equa on was developed using a hybrid ar ficial neural network -gene c algorithm approach that has been described elsewhere. Briefly, this approach permits a gene c algorithm approach to match an n-variable equa on that has been determined using the flexible ar ficial neural network to a n-variable phenomenological equa on that has been postulated based upon known physics. The resul ng equa on overcomes several of the limita ons of ar ficial neural networks, including devia ons in the equa on in regions of data sparsity. This equa on, originally developed for wrought Ti-6Al-4V, was modified slightly for the addi vely manufactured material. Specifically, a texture debit term was introduced for the observed decrease in yield strength along the primary x-y-z cartesian coordinate axis, and a Taylor hardening terms incorporated for varia ons in disloca on density.
A sophis cated sta s cal approach was incorporated to manage the small variability that exists between the predicted values and the experimentally measured values when both simulated and experimentally measured data is plo�ed on a cumula ve probability distribu on func on plot (c-pdf). A sta s cal adjustment of the model data and experimental data is sufficient to apply to future data and have such future data lie almost perfectly on the c-pdf.
In parallel, an ABAQUS code was developed to predict: the thermal history; the chemistry varia on due to vola liza on of certain species under vacuum; the microstructure; and the resul ng sta c mechanical proper es. The predicted c-pdfs were compared to the measured c-pdfs and found to be in very good agreement.

Results and Discussion
The results of this work are extensive, and too broad to appear in this proceedings paper. For complete descrip ons, the reader is pointed elsewhere [3][4][5][6]. The most important details of this work are given below.

The Equa on:
The phenomenological equa on that permits the predic on of the yield strength of Ti-6Al-4V is given below. The equa on is built upon the summa on of the individual strength contribu ons, star ng with the average intrinsic flow stresses of the hcpalpha and bccbeta phases, followed by composi onal increases to strength (i.e., solid solu on and inters al strengthening from Al, V, O, and Fe), followed by Hall-Petch related terms, a modifica on due to texture, and Taylor hardening. This equa on has been used to predict accurately the strength of wrought and addi vely manufactured Ti-6Al-4V, with varia ons in chemistry, including custom varia ons beyond the form of the equa on presented here. The variables are phase frac on, morphological dimensions, and composi onal terms [5].

Composi onal Varia ons:
In addi ve manufacturing, the molten pool can be quite hot. When this pool is present under an inert gas, it is possible that the molten pool will ge�er trace amounts of elements in the inert gas (i.e., O, N, H). When this pool is under vacuum, certain alloying species will be preferen ally lost to the vacuum. For Ti-6Al-4V, this preferen al vola liza on reduces the concentra on of aluminum. A reasonable model to predict the loss of aluminum (or the uptake of O, N, H under posi ve pressures) is based upon a model proposed by Langmuir, which predicts the mass loss across a given interface, and which has been adopted elsewhere [7][8][9]. In this model, it is important to know the temperature of the molten pool, the me a given surface will be available to mediate mass flux, and the area of the molten pool. Interes ngly, for addi vely manufactured materials, the calcula on of solute profiles in the liquid pool using, for example, Fick's Second Law, are not necessary, as the convec ve mo on of the liquid is quite high (~0.5 to 1.0 m/s), causing the solute to be ac vely redistributed in the liquid state, and thus enabling a simple mass-loss model. The simple Langmuir equa on is given below: where m is the mass of atoms entering or exi ng a surface, M i is the molecular weight, and p i is the par al pressure of species i.

Microstructural Varia on and Effects of Texture:
During solidifica on under vacuum, the size of the molten pool (~10 to 15mm in diameter) is sufficiently large so as to promote mul ple compe ng solidifica on fronts, especially in thick sec ons. These mul ple solidifica on fronts lead to a "bamboo" like appearance (see Fig. 1), where some grains are epitaxially grown from an underlying layer, and adjacent grains are nucleated from the adjacent AM passes side surface. This results in a microstructures varia on that is observable at the mesoscale (~1 cm frequency) but not at the microscale. This feature may be associated with signal complica ons when such specimens are subjected to nondestruc ve tes ng such as ultrasonic inspec on. Subscale test coupons were extracted from the different zones of this periodic bamboo structure. The tests of the ver cally banded regions resulted in mechanical proper es that had very li�le sca�er, whereas the ver cal bands consis ng of horizontally growing grains have a more random grain structure, and the corresponding mechanical proper es are more broadly sca�ered.
The appearance of this par cular feature drove the team to find alterna ve methods of materials characteriza on at the mesoscale. The authors are working with researchers at the University of No ngham (U.K.) to apply a new method of orienta on microscopy -spa ally resolved acous c spectroscopy (SRAS)-to these complicated structures. SRAS uses laser-induced surface acous c waves and a rela vely complex forward model to determine the local crystal orienta on. The maps that are achievable using SRAS are quite large, with demonstra ons of analysis over 20,000 square millimeters. One sub scale SRAS dataset is shown in Fig. 2(a), which clearly shows the banding structure. A large area run is shown in Fig. 2(b).
The strong {001} beta growth texture, along with the concomitant alpha variant selec on, results in the so�est crystallographic direc ons lying on planes oriented 45° away from the primary cartesian coordinate axes (x, y, z). A test of 36 coupons (6 for each of the primary axes (x, y, z) and 6 for each 45° off-axis test (xy, yz, xz)) clearly demonstrated that the tests taken along the primary axes exhibit yield strengths ~5.5% lower than the 45° counterparts [5].

Disloca on Densi es:
One important contribu on to strength in addi vely manufactured materials is Taylor Hardening. The disloca on densi es have been measured for different material thermal treatments following deposi on, and ranges from rela vely low values (~10 12 m -2 ) to rela vely high values (~10 15 m -2 ). This difference leads to a varia on in the yield strength of the material, as well as a slight reduc on in duc lity. An image showing a PED map and the corresponding disloca on density map for the stress relieved material is shown in Fig. 3. We note, rather importantly, that residual stress and average disloca on density are two different measurements. Residual stress is considered to be the spa al gradient in disloca on density. Thus, it is possible to have a high average disloca on density, but a low residual stress if the gradient is low. This is an important considera on for addi vely manufactured materials. We note that, currently, we do not have defini ve proof on the origins of such high disloca on densi es, but are pursuing a few theories.

Figure 3: PED and GND map [5]
Integrated Model: An ABAQUS model was developed that simulated the EBAM process, and integrated the multiple levels of physics that was required to predict the properties and performance. In addition to predicting composition, microstructure was predicted using two approaches, namely a phase field model and a database strategy. Similarly, the dislocation density was incorporated using a database approach. Following the linkage of these databases and the ABAQUS model, a series of "virtual tensile" coupons were made on the virtual depositions, and the populations compared with what was experimentally measured. The results are in excellent agreement, and shown in Fig. 4.

Conclusion
An ICME framework has been established to predict the sta c strength proper es and their cumula ve probabili es to predict performance for electron beam addi vely manufactured Ti-6Al-4V. Important factors in the strength model include composi on, texture, disloca on density, and the microstructures features. Once developed, the models are able to predict the tensile strength within ~1ksi (~7MPa).