Data Driven Tools and Methods for Microtexture Classification and Dwell Fatigue Life Prediction in Dual Phase Titanium Alloys

Microtexture has been linked to large reduc ons in cold dwell fa gue (CDF) life of specific dual phase tanium alloy aeroengine components. A recently completed Metals Affordability Ini a ve (MAI) funded program led by Pra� & Whitney (P&W) and includes ATI Forged Products, Boeing, GE Avia on, Rolls Royce (RR), Arconic, Titanium Metals Corpora on (TIMET), PCC-Wyman Gordon (PCC-WG), Scien fic Forming Technologies (SFTC), Materials Resources LLC (MRL) and The Ohio State University (OSU) has developed improved techniques for the characteriza on of microtexured regions (MTR) in tanium billet and forgings, and integrated computa onal materials engineering (ICME). These methods are aimed at developing and integra ng process and property modeling tools for the predic on of microtexture and fa gue life in tanium components. These characteriza on and fa gue life predic on tools have near-term applica on off ramps that will enable use for process and product development and quality control. Key results for two widely used alloys, Ti-6242 and Ti64, will be reviewed in this paper. Introduction The a+b class of tanium alloys are widely used in the fan and compressor stages of jet engines, due to their excellent strength to weight ra o and corrosion resistance. However, near a and a+b alloys such as Ti-6242 and Ti-6-4 have exhibited sensi vity to cold dwell fa gue, associated with cracking of microstructural regions that are unfavorably oriented for slip, also known as hard orientated grains [1-3]. Bache proposed a modified Stroh Model where disloca ons pile ups in grains favorably oriented for slip, i.e., so� grains, result in stress concentra ons along grain boundaries with neighboring hard oriented grains, ul mately ini a ng a crack [4]. Venkatramini, Ghosh and Mills later validated this proposal using a mul -scale computa onal finite element approach that iden fied a local phenomenon of load shedding, due to so� grains shedding load on to hard grains, with a significant rise in stress gradients across the interface [5]. Such stress redistribu on between microtextural regions with different crystal orienta ons has been proposed as the fundamental cause of the development of cracks during dwell fa gue in near a tanium alloys. © 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/). MATEC Web of Conferences 321, 11091 (2020) https://doi.org/10.1051/matecconf/202032111091 The 14 World Conference on Titanium


Introduction
The a+b class of tanium alloys are widely used in the fan and compressor stages of jet engines, due to their excellent strength to weight ra o and corrosion resistance. However, near a and a+b alloys such as Ti-6242 and Ti-6-4 have exhibited sensi vity to cold dwell fa gue, associated with cracking of microstructural regions that are unfavorably oriented for slip, also known as hard orientated grains [1][2][3].
Bache proposed a modified Stroh Model where disloca ons pile ups in grains favorably oriented for slip, i.e., so� grains, result in stress concentra ons along grain boundaries with neighboring hard oriented grains, ul mately ini a ng a crack [4]. Venkatramini, Ghosh and Mills later validated this proposal using a mul -scale computa onal finite element approach that iden fied a local phenomenon of load shedding, due to so� grains shedding load on to hard grains, with a significant rise in stress gradients across the interface [5]. Such stress redistribu on between microtextural regions with different crystal orienta ons has been proposed as the fundamental cause of the development of cracks during dwell fa gue in near a tanium alloys.
At the 1995 World Titanium conference, Woodfield et. al., presented their work on the rela onship between microstructure, microtexture and dwell fa gue in a+b processed Ti-6242 [6]. This seminal study used the electron backsca�er diffrac on (EBSD) technique to quan fy microstructure and microtexture parameters effec ng dwell fa gue life. The current study was aimed at evalua ng the dwell fa gue sensi vity in a+b alloys such as Ti-6-4 and developing and valida ng an open method for classifying and quan fying microtextured regions (MTR's) that can be u lized across the supply chain for the safe design and manufacture of tanium components.
This ar cle provides a review of the Air Force funded, Metals Affordability Ini a ve (MAI) PW-9 program on "ICME of Microtexture Evolu on and its Effect on Cold Dwell/High/Low Cycle Fa gue Behavior of Dual Phase Titanium Alloys", which is aimed at developing and integra ng process and property modeling tools and methods for the characteriza on and predic on of microtexture and fa gue life in dual phase tanium alloy components.

Experimental Procedure
In order to build robust fa gue models that capture a range of commonly observed microstructures and microtextures, the AIPT u lized produc on scale and lab-scale Ti-6-4 and Ti-6242 billet manufactured to various diameters. These billets were subsequently isothermally and non-isothermally forged at 50 o F below the b-transus, to various upset reduc ons, followed by an a+b solu on treatment and age that results in a primary a frac on between 30-55%.
DEFORM-2D finite element (FE) forge simula ons of the upset opera ons were conducted, and subsequently used to select fa gue sample blank loca ons. A total of 152 fa gue blanks -from Ti-6-4 pancakes and Ti-6242 pancakes -were extracted, machined, and peened. The fa gue samples were peened using S70 steel shot at an intensity between 45 to 85 psi. Dwell low cycle fa gue (DLCF) and con nuous low cycle fa gue (LCF) test coupon pairs were extracted from every major strain level contour in the pancakes, as shown in Figure 1. This ensured a good distribu on of MTR sizes and intensity levels in the fa gue samples. All the fa gue tests were run at an R=0 and maximum steady stress levels ranging between 120 to 132 KSI, with the addi on of a 2 minute tensile dwell me added to the DLCF tests. In addi on, a total of 74 room temperature tensile tests were also conducted according to ASTM E8 from blanks extracted from these Ti-6-4 and Ti-6242 pancakes. In order to adequately capture the morphological and texture characteristics of microtextured regions within the samples it was necessary to capture large scans covering several square millimeters. Electron backscatter diffraction (EBSD) was conducted on DLCF samples, sectioned along the longitudinal axis, to produce inverse pole figure maps and pole figures as well as texture data for subsequent MTR identification and quantification. A step size of 5µm was used to balance resolution of microtextured regions with scan duration. A few of these scans are summarized in Figure 2. For reference, the tensile stress axis runs horizontally through the images referred to as the [010] IPF direction. Significant qualitative differences were observed in the overall level of microtexture present. A major project goal was to develop tools and methods (T&M's) for the industrial supply chain to use for iden fica on and quan fica on of MTR's. Two T&M's were developed that u lized the large-area EBSD data detailed previously. The first T&M applied MRL's commercial so�ware, TiZone TM , for the iden fica on of MTRs through successive clustering of data points by orienta on and spa al loca on, followed by the segmenta on of iden fied MTRs into orienta on "classes" based on C-axis orienta on and finally genera ng metrics based on n-point sta s cs of each MTR class, including size, aspect ra o, and area frac on. MRL's methods were described in detail at the 13th Ti-World conference in San Diego [7].The second T&M u lized the open source so�ware, Dream3D, with program developed pipelines to import and clean EBSD data, segment features based on pixel misorienta on, and store the data in an efficient HDF5 format. The Dream3D so�ware by itself outputs metrics like feature size, average misorienta on, Euler angles, etc. MATLAB developed postprocessing scripts were subsequently used to compute addi onal metrics, like feature stress axis misalignment, density, intensity, degree of spa al clustering, and hard/so�/ini ator class labels, among others (Figure 3). The standard MTR parameters and values used for the PW9 program are shown in Table 1, which highlights the minimum size of an MTR, as well as the stress-axis misalignment values used for classifica on of hard, so�, and ini ator MTRs. In addi on, a single factor called MTR intensity, described in Equa on (1), that links three other parameters was used to compare the severity of microtexture levels between various material datasets manufactured in this program.
where I MTR is the MTR intensity, r is the density of similarly aligned alpha grains in an MTR, A is the MTR size and DC is the c-axis misalignment within an MTR.

Results and Discussion
LCF and DLCF results for Ti-6242 and Ti-6-4, shown in Figure 4, indicate a tendency for increased cyclic life in material containing lower microtexture levels. Analysis of the datasets suggests that a combination of good billet processing with higher forging strains result in higher fatigue lives. However, no strong effect of yield strength on fatigue life of Ti-6-4 and Ti-6242 was observed (Figure 5). These results suggest a complex inter-relationships between MTR metrics, test conditions, microstructure characteristics and dwell fatigue life of both alloys that were subsequently identified using machine learning tools. In addition, it was observed that dwell fatigue life of Ti-6-4 tested at equivalent percent yield strength levels were much shorter than for Ti-6242. This behavior is consistent with lower creep capability of Ti-6-4 compared with Ti-6242. Box plots of microtexture metrics were compiled for all MTRs greater than 10,000 um 2 , and were broken down by material process path (A to D), Figure 6. It is interesting to note quantifiable differences for MTR sizes and intensities between material process paths, which in-turn could enable quantified manufacturing process parameter requirements. Eureqa (R) , a commercially available software that automatically builds models, was used to calibate and validate a model that explicitly captured the influence of MTR metrics on fatigue life. A total of 59 DLCF tests were used to develop life models in Eureqa -80 percent of the data was used for model training and 20 percent for model validation. Over 70 statistically based microstructure and microtexture parameters along with the maximum stress as a function of yield strength were used to identify the critical parameters that correlate with dwell fatigue life for these 59 datasets. Eureqa splits datasets into a training dataset and a validation dataset in order to perform cross validation and prevent overfitting. Training data is used to generate and optimize solutions, and the validation set is used to test how well those models generalize to new data.
A total of five Eureqa models that had similar model errors were chosen for predicting sample dwell life. The mathematical relationships in these models were automatically generated by Eureqa, each having slightly different formulations and generalization capability over the testing range. Eureqa successfully identified 3 MTR metrics, along with the percent yield strength of the dwell test, as critical model inputs for DLCF life prediction (Figure 7). These results suggest that higher test stress levels and larger soft MTR sizes negatively impact DLCF life. In contrast, a larger fraction of soft MTRs and miscellaneous grains positively influence DLCF life. The significance of large soft MTRs is supported by many studies on dwell fatigue behavior in titanium alloys, which suggest that high stresses are developed at the interface between large soft MTRs that accommodate slip and hard MTRs that do not deform, leading to crack initiation and life shortfalls. On the other hand, having a large fraction of soft and randomly oriented grains will help to homogenize the strain distribution and improve life. All five Eureqa models were chosen for comparing sample dwell life prediction with measured failure life cycles. Figure 8 shows that all the predictions, except one, were within a 2X life bounds. This Ti-6-4 outlier had an extremely low life but contained average MTR metrics. Once the critical MTR model input parameters were identified and DLCF life model were generated, Eureqa was used to develop models linking forge parameters to MTR evolution from billet to pancakes. This was accomplished by using starting billet MTR metrics together with forging temperature and location based effective strains that correspond to DLCF samples in the pancake. The strain levels were previously determined using DEFORM simulations of the pancake process. Results of predictions showed that about 10 of 59 predicted datasets lay outside the 2X life bounds.

Summary
The PW-9 program successfully developed critical tools and methods for implementation in the supply chain. These tools will support the design of manufacturing processes and final components, as described below:

EBSD based tools and methods to iden fy, classify and quan fy MTRs
Large datasets comprising of area scans spanning 8mm x 8mm were used to capture MTRs. An open source so�ware, Dream3D, was u lized to import and clean EBSD data, segment features based on pixel misorienta on, and store the data in an efficient format. MATLAB post-processing scripts were subsequently used to compute addi onal MTR classifica on and quan fica on metrics.

Accurate Dwell fa gue life models for Ti-6-4 and Ti-6-2-4-2
Fa gue models for Ti-6-4 and Ti-6-2-4-2 were successfully validated using fa gue test parameters, microstructure and microtexture metrics. Mean life predic ons were within a factor of 2, and within the 95 percent confidence of the experimentally determined mean fa gue life. Analy c models that explicitly capture the influence of MTR metrics on fa gue life were also developed u lizing Eureqa. This approach captured three cri cal MTR characteris cs that significantly impact DLCF.