*2.1. Experiments*

Laser Engineered Net Shaping (known as LENS) [52–54] is the prototypical powder-blown direct energy deposition technique used for additive manufacturing. It often incorporates computer-controlled lasers as power sources and produces near-net shapes with sufficiently accurate dimensions as the final product [55] to eliminate the need for rough machining, making it popular in industry [52,53,56,57]. Due to characteristics such as its great reliability [53,54,58] and the low porosity [59–61] of the final products, LENS is widely employed in the customization and repair of intricate mechanical parts, including turbine blades [54,62–66]. The ability to control, independently, the powder flow from separate powder feeders in LENS allows for creating chemical gradients in the AM components [67–72]. This is of tremendous interest for the present study, which aims to prototype a large library of material samples of small volumes covering a range of alloy compositions and post-build heat treatments.

The binary Ti–xMn (x ranges from 0 to ~15 wt.% Mn) system was selected for this study. Titanium–manganese alloys are of great interest because of their numerous applications in aerospace, hydrogen storage and biomedical industries [73–75]. This range of manganese content in the alloy introduces a typical eutectoid β-stabilized system [73,76,77] that is notoriously susceptible to the segregation defect during solidification, known as "β-fleck" [78–81], and thus not suitable for traditional ways of developing cast/wrought titanium alloys. AM has the potential to eliminate β-fleck by taking advantage of the high thermal gradients and small molten pools, thereby reducing liquid-phase separation. By eliminating β-fleck, it may be possible to subsequently increase the strength through post-build aging heat treatments. An Optomec 750 LENS system was utilized to produce samples in this work. Elemental powders of Ti and Mn were introduced into the molten pool using two independently and automatically controlled powder feeders, one containing pure Ti and the other containing a mixture of elemental Ti and elemental Mn with a composition of 15 wt.% Mn. These powders, after leaving their powder feeders at preset feed rates, were mixed and focused into the molten pool by a multi-nozzle system. A Nd:YAG laser system producing near-infrared radiation with a wavelength of 1064 nm was focused coincident to the focal point of the powder, generating a local molten pool where melting and mixing occurred. The motion of the build plate was then controlled so that thin layers of controlled composition were deposited with predetermined width and thickness. The laser power at the molten pool was 410 W, and the nominal flow rate of the powders was ~2.6 g/min. The substrate travel speed (equivalent to the laser scan speed, but with a different reference frame) was 10 inch/min (the nonstandard units of inches and minutes are used when describing build parameters, as these are the standard units of the Optomec control system itself), and the hatch widths and layer thicknesses were 0.018 inch and 0.010 inch, respectively. The oxygen content in the glove box was maintained below 10 parts per million, with the balance being primarily argon gas.

Cylindrical samples with compositional gradients along their length were produced (see Figure 1a). Planning for the potential loss of volume of material due to cutting/machining/sample preparation (e.g., through the curfs of cuts), a small number of layers were programed to have the same composition at the beginning and end of the depositions. As a result, the samples produced for this study showed Mn content ranging from 0 to ~12 wt.% along the length. Three long strips (see the strip dimensions in Figure 1b) were sectioned out of the cylindrical sample and were subjected to different aging treatments. The aging treatments selected for the study included three different temperatures (500, 600 and 700 ◦C; see Figure 1c), while the aging time was kept the same, at four hours. The post-build aging treatment is expected to release residual stresses (these can be significant in the LENS technique due to the high power of the energy source, subsequent high temperature of the melt pool, fast cooling process

and high build rate) as well as significantly alter the phase volume fractions and phase morphology, promoting possibilities of attaining improved properties.

– – **Figure 1.** (**a**) Illustration of the layered Ti–Mn cylindrical sample manufactured by the Laser Engineered Net Shaping (LENS) process in this study. (**b**) Sample strip sectioned from (**a**) with compositional gradient along the length of the sample. Five locations were chosen longitudinally in each sample strip for characterization. They were 8, 14, 20, 26 and 32 mm away from the pure titanium end of the strip (labeled as #1–#5, respectively). (**c**) Three different sample strips were aged at three different temperatures (500, 600 and 700 ◦C, respectively) for four hours to produce the sample library used in this work. (**d**) A grid of indentation and microscopy characterization was performed at each location illustrated in (**b**). Each circle represents an indentation testing site, while the square represents the microscopy characterization site. Each measurement grid contained 5 by 5 indentation tests and the same number of microscopy characterizations. The test points in the grid were evenly spaced at 100 µm. Note all test sites shown in (**b**) are intentionally kept away from the thin end of the sample strips, making sure the sample has at least 2 mm thickness at the indentation test sites.

– After aging, all the sample strips were prepared for microscopy and spherical indentation stress–strain measurements using standard metallography protocols established previously for titanium alloys [82]. These included grinding (P240 and P1200 SiC papers), followed by polishing steps with decreasing abrasive particle sizes (9, 3 and 1 µm diamond suspensions), while making sure every step removed the surface deformation introduced by the previous step. A solution of 0.06 µm colloidal silica suspension with hydrogen peroxide in the ratio of 5 to 1 was employed in a final polishing step to produce the desired surfaces for microscopy and indentation.

The main focus of this study is exploring high-throughput experimental assays for exploring large material spaces for AM. Five locations were selected longitudinally in each sample strip (see Figure 1b) for microstructure characterization and indentation tests. The transverse directions on the sample surface are not expected to exhibit any significant compositional gradients. Multiple indentation measurements and back-scattered electron (BSE) imaging were performed on a 5 × 5 grid at each

of the five selected locations (illustrated in Figure 1d). Indentation tests were performed on an Agilent G200 (Santa Clara, CA, USA) with a continuous stiffness measurement (CSM) under a constant strain rate of 0.05/s and 800 nm indentation depth. The CSM was set at a 45 Hz oscillation with a 2 nm displacement amplitude [83]. A Tescan Mira XMH field emission SEM (Warrendale, PA, USA) with a 20 kV accelerating voltage was used to capture back-scattered electron (BSE) images. Energy dispersive spectroscopy (EDS) was performed at the five locations shown in Figure 1b to measure the Mn content. At each location, five EDS measurements randomly distributed within the 5 × 5 grid (established in Figure 1d) were performed. Each measurement was carried out by first mapping the element concentration distribution of a 50 µm × 50 µm area and then calculating the average element composition according to the map. A Hitachi SU8230 SEM (Tokyo, Japan) equipped with Oxford EDAX and Aztec analysis software was used for EDS analysis. Beam calibrations with a 100% copper plate were used for EDS quantification. The accelerating voltage was kept at 20 kV and beam intensity at 20 µA for these measurements.

#### *2.2. Microstructure Analysis and Quantification*

The two-phase BSE images were segmented with Otsu's method [84,85]. Otsu's method separates the intensity distribution of an image into two classes by using a threshold. The threshold value is determined to maximize the interclass variance (or minimize the intraclass variance). Otsu's thresholding was performed using the "graythresh" function of the numerical computing software MATLAB [86]. The segmented (binary) images were used to compute the volume fraction of the β phase. Additionally, averaged chord lengths (CL) [87,88] were computed to quantify the length scales of the α and β phase regions in the microstructure. The procedures used to identify the chords are based on pixelized representations of the images and have been described in prior work [87,89]. A chord is defined as a line segment (measured as the number of pixels) that completely lies inside a distinct material phase, whose extension in any direction by even one pixel encounters pixels of a different material phase.

#### *2.3. Mechanical Characterization*

The spherical indentation stress–strain protocols [90–92] employed in this study are built largely on Hertz's theory [93,94] for elastic frictionless contact between two isotropic bodies with parabolic surfaces (see Figure 2a). The relevant relationships are summarized below:

$$P = \frac{4}{3} \mathcal{E}\_{eff} \mathcal{R}\_{eff}{}^{1/2} h\_e^{3/2} \tag{1}$$

$$a = \sqrt{\mathcal{R}\_{eff} h\_\ell} = \frac{\mathcal{S}}{2\mathcal{E}\_{eff}}\tag{2}$$

$$\frac{1}{E\_{eff}} = \frac{1 - v\_i^2}{E\_i} + \frac{1 - v\_s^2}{E\_s} \tag{3}$$

$$\frac{1}{R\_{eff}} = \frac{1}{R\_i} + \frac{1}{R\_s} \tag{4}$$

where *P* and *h<sup>e</sup>* denote the indentation load and elastic indentation displacement, *Ee f f* and *Re f f* denote the effective modulus and the radius of the indenter-sample system, subscripts *i* and *s* correspond to the indenter and the sample, and the Young's modulus and Poisson's ratio are denoted as *E* and ν. In Equation (2), *S* (= *dP*/*dhe*) denotes the elastic stiffness (also known as the harmonic stiffness in continuous stiffness measurement (CSM) protocols [83,95,96]). Building on these relationships, one can define the indentation stress, σ*ind*, and the total indentation strain (includes the elastic and plastic strains), ε*ind*, as

$$
\sigma\_{\rm ind} = \frac{P}{\pi a^2} \tag{5}
$$

*Materials* **2020**, *13*, 4641 the Young's modulus are related as

–

$$
\varepsilon\_{\rm ind} = \frac{4}{3\pi} \frac{h\_{\rm s}}{a} \tag{6}
$$

–

where *h<sup>s</sup>* is the corrected sample displacement (subtracting the displacement in the indenter, *h<sup>i</sup>* , from the total displacement, *h*) and is computed using – –

=

ℎ = ℎ −

ℎ

4 3 ℎ ℎ ℎ

> 3(1 − 2 )

> > 4

$$h\_s = h - \frac{3\left(1 - v\_i^2\right)P}{4E\_i a} \tag{7}$$

– – **Figure 2.** (**a**) Illustration of spherical indentation. (**b**) Indentation stress–strain curve acquired from Location #4 (see Figure 1b) of the strip heat treated at 700 ◦C. The slope illustrated in the elastic portion of the indentation stress–strain curve is the effective modulus, *Ee f f* . The red dot represents the indentation yield strength *Yind* corresponding to a 0.002 offset indentation plastic strain, while the black segment (from 0.005 to 0.02 in offset indentation plastic strain) represents the data used to estimate the indentation work hardening rate *Hind* .

 The indentation stress and indentation strain defined in Equations (5) and (6) exhibit a linear relationship in purely elastic indentations, where the slope of the indentation stress–strain curve is referred to as the indentation modulus, *Eind* . For an isotropic material, the indentation modulus and the Young's modulus are related as

$$E\_{ind} = \frac{E\_s}{\left(1 - \nu\_s^2\right)}\tag{8}$$

On the indentation stress–strain curve (see Figure 2b), a 0.2% offset indentation plastic strain is used to define the indentation yield strength, *Yind* . The indentation stress–strain curve between the 0.5% and 2% offset indentation plastic strains is fitted with a linear regression [82,97] to compute the indentation work hardening rate, *Hind* . In prior work [82,91,98,99], Equations (5) and (6) were demonstrated to produce meaningful elastic–plastic indentation stress–strain curves that show an elastic–plastic regime following an initial elastic regime (see Figure 2b).

In the present study, spherical indentations on a 5 × 5 grid were performed with a uniform spacing of 100 µm (see Figure 1d). A diamond indenter tip with a nominal radius of 100 µm was used in all the tests reported in this work. Each indentation produced a contact area of about 150 µm<sup>2</sup> (contact radius of roughly 7 µm) at indentation yield and hence reflected the effective response of the two-phase microstructures obtained in the sample library (micrographs presented later). The spacing between indentations was designed to be large enough to minimize the interference between neighboring indentations. However, it was also important to keep the spacing small enough so that the compositional variation between the indentation locations within each grid was very small.
