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Materials Science & Engineering A 799 (2021) 140154

Available online 28 August 2020

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Materials Science & Engineering A

journal homepage: www.elsevier.com/locate/msea

Mechanical anisotropy of additively manufactured stainless steel 316L: An

experimental and numerical study

A. Charmi∗, R. Falkenberg, L. Ávila, G. Mohr, K. Sommer, A. Ulbricht, M. Sprengel,

R. Saliwan Neumann, B. Skrotzki, A. Evans

BAM, Bundesanstalt für Materialforschung und -prüfung, Unter den Eichen 87, 12205 Berlin, Germany

ARTICLE INFO

Keywords:

Mechanical anisotropy

Residual stress

Crystal plasticity

Selective laser melting (SLM)

Laser beam melting (LBM)

ABSTRACT

The underlying cause of mechanical anisotropy in additively manufactured (AM) parts is not yet fully

understood and has been attributed to several different factors like microstructural defects, residual stresses,

melt pool boundaries, crystallographic and morphological textures. To better understand the main contributing

factor to the mechanical anisotropy of AM stainless steel 316L, bulk specimens were fabricated via laser

powder bed fusion (LPBF). Tensile specimens were machined from these AM bulk materials for three different

inclinations: 0◦,45◦, and 90◦relative to the build plate. Dynamic Young’s modulus measurements and tensile

tests were used to determine the mechanical anisotropy. Some tensile specimens were also subjected to residual

stress measurement via neutron diffraction, porosity determination with X-ray micro-computed tomography

(μCT), and texture analysis with electron backscatter diffraction (EBSD). These investigations revealed that

the specimens exhibited near full density and the detected defects were spherical. Furthermore, the residual

stresses in the loading direction were between −74 ± 24 MPa and 137 ± 20 MPa, and the EBSD measurements

showed a preferential ⟨110⟩orientation parallel to the build direction. A crystal plasticity model was used

to analyze the elastic anisotropy and the anisotropic yield behavior of the AM specimens, and it was able to

capture and predict the experimental behavior accurately. Overall, it was shown that the mechanical anisotropy

of the tested specimens was mainly influenced by the crystallographic texture.

1. Introduction

Additive manufacturing describes layerwise production processes

that incrementally build structures from a feedstock material. Laser

powder bed fusion (LPBF) is an example of additive manufacturing

whereby structures are built in a repeated layerwise fashion via laser-

induced localized melting and solidification of a metal powder bed

feedstock. These processes offer significantly greater freedom of design

compared to conventional subtractive manufacturing processes, with

the potential for improved efficiency and functionality [1]. However,

despite the technological improvements made in recent years, metal ad-

ditive manufacturing, also known as metal 3D printing, still faces many

different challenges such as microstructural defects, residual stresses

(RSs), mechanical anisotropy and in general lack of understanding

of process-property-performance relationship [2–4]. These issues are

reported to prevent additive manufacturing from mass adoption in

safety-critical environments [5].

Stainless steel 316L specimens produced via laser powder bed fusion

(LPBF316L) usually have a layered morphology, which consists of many

different features on a broad range of length scales [6,7]. Additively

∗Corresponding author.

E-mail address: [email protected] (A. Charmi).

manufactured (AM) alloys and, in particular, LPBF316L have been

reported to exhibit anisotropic mechanical properties. The cause of the

anisotropic behavior of LPBF316L has been attributed to many different

factors. The consequence of layer-by-layer manufacturing, particularly

the interface between layers, is one of the more frequently mentioned

causes, since oxidation, inclusions, and defects are more frequent in

these regions [8–10]. The grain size, grain shape, and grain aspect ratio,

in combination with the Hall–Petch effect [11,12], have also been cited

as the source of anisotropy in LPBF316L [10,13–15]. The explanation

which is usually given for this effect is that the high angle grain

boundaries are a major barrier for dislocation glide, and since the dislo-

cations have to cross a different number of grain boundaries in various

directions, this results in an anisotropic behavior. However, several au-

thors [6,16,17] consider that the mechanical performance of LPBF316L

is mainly determined by its subgrain structures, predominantly the

fine-scaled dendritic microstructure, and not by the high angle grain

boundaries. Many other research groups reported finding these highly

oriented cellular microstructures for different sets of process parame-

ters [6,8,17–22]. RSs [23–27] and melt pool boundaries [28] may also

https://doi.org/10.1016/j.msea.2020.140154

Received 22 June 2020; Received in revised form 24 August 2020; Accepted 25 August 2020

Materials Science & Engineering A 799 (2021) 140154

A. Charmi et al.

be contributing to the anisotropy of LPBF316L specimens. Crystallo-

graphic texture has been repeatedly associated with the mechanical

anisotropy of LPBF316L [2,15,29,30]. Moreover, the authors of [13,

17,19,31,32] consider the combination of crystallographic texture and

different deformation mechanisms, mainly dislocation slip and twin-

ning, responsible for the directional dependency of material behavior.

They argue that for certain specific crystallographic directions defined

by the texture, either twinning or dislocation glide are more favorable.

Thus, depending on the loading direction, one of the competing mech-

anisms will dominate the deformation behavior. The authors of [26]

investigated the mechanical anisotropy of LPBF316L and compared the

results with previous studies. They reported that the observations con-

cerning the orientation dependency of the material behavior differed

significantly and even contradictory. For example, in many cases, the

highest elongations to failure were obtained in specimens with parallel

layers to the loading direction, but in some cases, the specimens with

perpendicular layers to the loading direction had the highest elongation

after fracture. The dependency of ultimate tensile strength on loading

direction also showed no clear tendency [26].

Based on the state of the research, it can be summarized that the

underlying cause of anisotropy and the numerical modeling aspect

of it in LPBF requires further investigation. Having a better under-

standing of the origin of anisotropy in LPBF316L is beneficial to the

additive manufacturing community when dealing with this issue. Many

applications like topology optimization [33,34], modeling of lattice

structures [35], and simulation of thermophysical processes during

additive manufacturing [36] are heavily influenced by the anisotropy.

Hence, the findings in this work could help remedy some of the existing

shortcomings and improve modeling accuracy. Therefore, the objective

of this paper concerns the determination of the main contributing factor

to the mechanical anisotropy of LPBF316L. This investigation was

conducted, combining both experimental and numerical methods. Me-

chanical testing combined with dynamic Young’s modulus determina-

tion, RS measurements via neutron diffraction, porosity measurements

with X-ray micro computed tomography (μCT), and texture analysis

with electron backscatter diffraction (EBSD) were used to characterize

the material. Numerical simulations were employed to investigate the

mechanical anisotropy by only considering the influence of crystal-

lographic texture. Moreover, the comparison between experimental

and simulated stress–strain curves will demonstrate the capability of

the numerical methods to capture and predict the material behavior

accurately.

2. Experimental methods

2.1. Material and laser powder bed fusion processing conditions

A commercial LPBF system SLM280HL (SLM Solutions Group AG,

Germany), equipped with a single 400 W continuous wave ytterbium

fiber laser, was utilized to produce specimens using 316L stainless steel

powder feedstock. The commercially available gas atomized 316L raw

powder can be described by an apparent density of 4.58 g/cm3, and a

mean diameter of 34.69 μm according to the supplier information. The

cumulative mass values of the particle size distribution were: D10 =

18.22 μm, D50 = 30.50 μm and D90 = 55.87 μm. More details about the

powder can be taken from [37,38]. The laser melting processes were

conducted in argon gas atmosphere at an oxygen content below 0.1%.

The stainless steel base plates were heated up to a temperature of 100 ◦C

before and during the process. The following process parameters were

used for all specimens: layer thickness of 50 μm, scanning velocity of

700 mm/s, laser power of 275 W and hatch distance of 0.12 mm. An

alternating meander stripe scanning strategy was applied. The scanning

pattern was rotated by 90◦from layer to layer. Two types of specimens

were manufactured in three different build processes: walls of the

dimensions (13 × 80 × 80) mm3and towers of the dimensions (13 × 20 ×

112) mm3, see Figs. 1 and 2. The walls were manufactured upright,

Table 1

Overview of all test specimens. Two tensile specimens were manufactured for each load-

ing direction except for the Tower 90◦. Young’s modulus specimens were manufactured

from a single wall.

0◦45◦90◦

Tensile specimens from tower 2 specimens 2 specimens 1 specimen

Tensile specimens from wall 2 specimens 2 specimens 2 specimens

Young’s modulus specimens 1 specimen 1 specimen 1 specimen

the dimension in build direction (Z-Axis) was 82.5mm in order to

compensate for cutting waste during part removal. The towers were

manufactured for three different inclinations: 0◦(Z-Axis dimension

22.5mm), 45◦(Z-Axis dimension 90.9mm) and 90◦(Z-Axis dimension

114.5mm) relative to the build plate. The scan vectors proceeded

parallel to the edges of the 45◦towers and 90◦towers over the full

length of the part without being split into different sections. For the

walls and 0◦towers, the scanning vectors proceeded in an angle of

45◦to the edges of the respective geometry to avoid high RSs at

long scanning vectors and to avoid splitting of scanning vectors into

stripes. For a graphical overview of produced geometries, used scan

strategies, and coordinate systems, see Fig. 1. The interlayer time (ILT)

was kept constant for all processes at a value of approximately 65 s

according to [37]. In cases of height differences of specimens that

were manufactured on the same base plate or differences in ratios of

area exploitations (RAE) between the different build processes, dummy

areas were scanned without laser power. All specimens were heat-

treated after the process and before removal from the plate at 450 ◦C

for 4h under argon gas atmosphere to relieve the RSs. This temperature

was chosen in order to avoid substantial changes in the microstructure.

2.2. Machining of test specimens

To experimentally investigate the mechanical anisotropy, tensile

specimens were manufactured from both walls and single towers for

three different inclinations, namely 0◦,45◦and 90◦. Dynamic Young’s

modulus specimens were only manufactured from the wall. In total,

five tensile specimens from five single towers, six tensile specimens

from two walls, and three Young’s modulus specimens from one wall

were produced. An overview of all test specimens can be seen in

Table 1. The tensile specimens from the single towers were machined

(turned and subsequently ground) from the middle region of each

tower. The walls were first symmetrically plane ground to a thickness

of 12 mm. Afterward, blocks with near-net dimensions were cut out

of the walls via wire electrical discharge machining (EDM). Fig. 3

shows the positions of these blocks, which were subsequently used

for producing tensile and Young’s modulus specimens. The Young’s

modulus specimens, which came from the bulk region of the walls (see

Fig. 3, on the left), were subjected to milling and surface grinding

in the last machining steps. The exact geometry of tensile specimens

can be seen in Fig. 3 on the right. The Young’s modulus specimens

have a dimension of (3 × 6 × 64) mm3with a rectangular cross-section

and plane parallelism between the opposite faces with ±1% accuracy.

The exact dimensions and weight of the latter specimens, needed for

the determination of the elastic properties, were determined with a

caliper gauge (Model CD-20D, accuracy: ±10 μm, Mitutoyo Deutschland

GmbH, Germany) and an outside micrometer (Model 232871, accuracy:

±1 μm, Vogel Germany GmbH, Germany) and with a precision balance

(accuracy: ±0.001 g, Sartorius AG, Germany) respectively.

2.3. Tensile testing

The tensile tests were conducted at room temperature according

to DIN EN ISO 6892-1 [39] (Method A, strain rate range 2) using

a100 kN Instron testing machine (Model: 4505, Instron GmbH, Ger-

many) calibrated according to DIN EN ISO 7500-1 [40] (Force, class

Materials Science & Engineering A 799 (2021) 140154

A. Charmi et al.

Fig. 1. Schematic portrayal of all geometries and the corresponding scan strategies. Note the rotated scan strategy for the Tower 0◦and wall specimens compared to the Tower

90◦and Tower 45◦specimens, which is a 45◦rotation about the Z-Axis. These changes were made to avoid high residual stresses and will directly impact the microstructure and

consequently, the material behavior, which will be further analyzed in the results and discussion section. The black (X, Y, Z)and blue (X′,Y′,Z′)coordinate systems will be used

for the texture analysis in Section 4.3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2. Tower and wall specimens produced during three build processes on (280 × 280) mm2base plates. The ILT for each build process was kept at a value of approx. 65 s to

ensure comparable thermal history and microstructure across all specimens.

1) and DIN EN ISO 9513 [41] (Displacement, class 1). The strain

was recorded using an extensometer (Model: 632.12C-21, MTS Systems

GmbH, Germany) with 25 mm gauge length, which was calibrated in

the range of −10% to 50% strain according to DIN EN ISO 9513 [41]

(class 0.5). Since all specimens failed before reaching the maximum

value of the extensometer measurement range, all tests were driven

entirely strain-controlled and switching to crosshead speed control was

not necessary.

2.4. Dynamic Young’s modulus determination

The determination of dynamic Young’s modulus was carried out at

room temperature according to ASTM E1876 [42]. An Industrial testing

machine (Model: GrindoSonic MK5, GrindoSonic BVBA, Belgium) and a

network analyzer (Model: HP8751A, Agilent Technologies, Inc., United

States) were used to perform these tests. In this technique, also called

the resonance method, the dynamic Young’s modulus is determined

using the fundamental resonance frequency, dimensions, and mass of

the test specimens. The dynamic elastic properties are measured under

oscillatory displacements, involving small strains, relatively high strain

rates, and adiabatic conditions. It should be noted that the elastic prop-

erties determined under adiabatic conditions exhibit slightly higher

values compared to the elastic properties determined under isothermal

conditions [43]. The resonance frequency is measured by exciting

the test specimens mechanically by a singular strike with an impulse

tool and then analyzing the electric signal generated by a transducer,

which senses the resulting mechanical vibrations of the specimen and

transforms them into an electrical signal. Dynamic techniques provide

an advantage over static methods because of greater precision, ease of

specimen preparation, and a wide variety of allowed specimen shapes

and sizes [44,45].

2.5. Porosity and defects analysis

Microstructural defects are believed by some researchers to play a

role in the mechanical anisotropy of AM specimens [8–10]. Therefore,

Materials Science & Engineering A 799 (2021) 140154

A. Charmi et al.

Fig. 3. Technical drawings of the test specimens. Position of extracted tensile and Young’s modulus specimens in the wall (shown on the left), which were cut out via EDM, and

the geometry of tensile specimens (shown on the right).

to assess this possibility within the scope of the process parameters

detailed in Section 2.1 and identify the overall quality of the manufac-

turing process, six of the cylindrical tensile specimens were analyzed for

porosity by μCT. Three of them were extracted from towers build with

an inclination towards the build plate of 0◦,45◦, and 90◦, respectively,

and three specimens were extracted from a wall with inclinations

of 0◦,45◦and 90◦. The data was acquired on the commercial μCT

scanner (Model: GE v|tome|x 180/300, Baker Hughes, United States)

using a voltage of 200 kV, a current of 50 μA and a silver prefilter of

0.25 mm thickness. The reconstructed datasets were analyzed using the

commercial software VG Studio MAX Version 3.2 (Volume Graphics

GmbH, Germany). Pores were segmented within a gauge length of

16 mm around the center of the specimens. Due to the achieved voxel

size of 10 μm, only defects larger than 20 μm could be segmented.

2.6. Residual stress measurements

The neutron diffraction experiments were performed using the

angular-dispersive diffractometer E3 at the Helmholtz Zentrum Berlin,

Germany, to determine the state of RSs in six tensile specimens and

further investigating their influence on material behavior. The detailed

set-up of the instrument can be found in [46]. A wavelength of ≈

1.476 Å and corresponding 2𝜃angle of 86◦were used to record the

Fe-311 reflection. The choice to use the {311} was made based on

the reported similar behavior with the bulk properties in the elastic

regime as well as its low tendency to form intergranular strains [47–

49]. In order to calculate the triaxial RSs, strains were determined

along three orthogonal orientations defined by the blank specimen

geometry and aligned to the specimen axis. Small cubes of dimension

(3 × 3 × 3) mm3were cut by wire EDM close to the gauge length of

the specimens extracted from the wall, from the respective specimen

blanks or from specimens located in the vicinity of the investigated

specimen to be used as the stress-free reference. The use of wire EDM

prevents the insertion of additional RSs, as the thin recast layer at the

surface is not sampled, and it is therefore assumed that the macroscopic

RSs are fully released in the cubes [48,50]. The stress-free reference

diffraction angles were measured in three orthogonal directions and

averaged for subsequent stress calculations to minimize the influence

of microscopic RSs. The RS distribution for the Tower 90◦tensile

specimen was acquired during two measurements, and an angular offset

of approximately 0.02◦related to the different experimental conditions

was applied for data merging. The Young’s modulus of 184 GPa and

Poisson’s ratio of 0.294 were calculated in [51] for the {311} reflection

assuming random texture using the model of Kröner [52] and measured

single-crystal elastic constants. RSs were then calculated using Hook’s

law:

𝜎𝑖𝑗 =𝐸ℎ𝑘𝑙

1 + 𝜈ℎ𝑘𝑙 (𝜀ℎ𝑘𝑙

𝑖𝑗 +𝜈ℎ𝑘𝑙

1−2𝜈ℎ𝑘𝑙 (𝜀ℎ𝑘𝑙

11 +𝜀ℎ𝑘𝑙

22 +𝜀ℎ𝑘𝑙

33 )),(1)

with 𝜎𝑖𝑗 referring to the stress, 𝐸ℎ𝑘𝑙 and 𝜈ℎ𝑘𝑙 the lattice plane spe-

cific Young’s modulus and Poisson’s ratio, and 𝜀ℎ𝑘𝑙

𝑖𝑗 the measured

strain. The isotropic condition was used per recently reported work on

LPBF316L [51]. However, it is noted that anisotropy of the diffraction

elastic constants (DECs) governed by non-random texture would exert

an effect on the calculated stresses, although the variation is not

considered in the values presented herein. The RSs were determined

using a diffraction gauge volume of (2×2×2) mm3in five measurement

positions on three planes distributed along the gauge volume of six

tensile specimens. The distance between each plane was 18 mm along

the gauge length. The locations of the measurement planes and points

in the tensile specimens are shown in Fig. 4. The neutron diffraction

data analysis was performed using the StressTexCalculator [53].

2.7. Electron backscatter diffraction measurements

For EBSD measurements all specimens were ground and polished:

Emery papers with 180,320,600 and 1200 grits were used, followed

by clothes with 3 μm and 1 μm particle suspensions. Subsequently, the

Materials Science & Engineering A 799 (2021) 140154

A. Charmi et al.

Fig. 4. Measurement planes and positions used during neutron diffraction experiments. The RSs were determined on three separate planes along the height of each specimen,

which are labeled as Bottom, Middle, and Top. On each plane, five positions were used for the measurements, which are shown on the right side. Note that the sample coordinate

system (X,Y,Z)is different from the coordinate system in Fig. 1 and it will be used to analyze the residual stresses in Section 4.2. In the sample coordinate system, X and Y are

always parallel to the edges of the produced geometry irrespective of the employed scan strategy. Furthermore, Z is always aligned with the loading axis.

specimens were electro-polished on Struers Lectropol-5 (Struers GmbH,

Germany) device using standard electrolyte A2. The measurements

were done on a scanning electron microscope (SEM) Leo Gemini 1530

VP (Carl Zeiss Microscopy GmbH, Germany) equipped with a high res-

olution EBSD detector e−FlashHR+ (Bruker Corporation, United States).

The software package ESPRIT 1.94 (Bruker Corporation, United States)

was used for acquisition, indexing and post-processing. The EBSD mea-

surements were done on specimens extracted from the middle section of

a Tower 90◦specimen, the top section of a Tower 45◦specimen, and on

specimens extracted from one of the walls. In total five different regions

were used for the EBSD measurements to extract the representative

crystallographic and morphological texture, see Fig. 5. The 70◦-tilted

samples were investigated using electrons of 20 kV energy. The further

settings for the measurements were 11.9 μm pixel size, 17 ms exposure

time, 10 nA beam current, and a pattern size of 160 ×120 pixels.

3. Numerical methods

3.1. Creation of representative volume elements

The simulations in this paper are conducted in a representative

volume element (RVE) framework. These RVEs equal the statistical

properties of the grain morphology and crystallographic texture, which

were extracted from the EBSD scans of the specimens. To simplify this

procedure and also isolate the influence of crystallographic texture on

the simulation results, the grain size distribution was replaced with a

cubic grain having a dimension of (70 × 70 × 70) μm3, see Fig. 6. This

grain aspect ratio and average grain size are chosen based on the EBSD

measurements and the resulting grain size distributions, see Figs. 9

and 11 in Section 4.3. The simulation results for these 3 RVEs were

compared to ensure convergence. The synthetic RVEs seen in Fig. 6

were generated with software Neper [54]. The crystallographic texture

was extracted from EBSD measurements using the MTEX software [55],

which outputs orientation distribution function (ODF) intensity data.

The ODFs, which were calculated using a 4.5◦halfwidth, were then

used in the hybridIA scheme [56] to find discrete sets of orientations

matching the number of grains in each RVE. The hybridIA scheme is

capable of reconstructing textures using only a few numbers of equally

weighted orientations, which is beneficial to the accuracy of crystal

plasticity (CP) simulations. In the last step, these extracted orientations

were randomly assigned to the Fourier points inside the RVEs.

3.2. Mechanical equilibrium

To obtain the equilibrium deformation field, the following equation

needs to be solved under a given set of periodic boundary conditions

applied to the RVEs:

Div𝐏= 0,(2)

where 𝐏is the first Piola–Kirchhoff stress tensor. The deformation

mapping 𝝌can be decomposed in a homogeneous deformation gradient



𝐅, and a superimposed deformation fluctuation field 

𝐰[57,58]

𝝌=

𝐅𝐱 +

𝐰,(3)

which satisfies the periodicity condition. Therefore, the deformation

gradient can be split into a homogeneous deformation gradient 

𝐅and

a locally fluctuating part 

𝐅

𝐅=

𝐅+

𝐅.(4)

The solution of the mechanical boundary value problem, expressed

in terms of the deformation gradient field, is obtained solving the

following system of equations [57,58]:

Fbasic [𝐅(𝐱)]∶= F−1 [{

(𝐤)𝐏(𝐤) = 𝟎if 𝐤≠0

𝛥𝐅BC if 𝐤= 0 ](5)

where 𝐱and 𝐤are position in real space and frequency vector in Fourier

space, respectively. For the sake of brevity, the reader is referred

for specifics about the Gamma operator

and the collocation-based

discretization approach necessary for obtaining Eq. (5) to [57], where

the spectral solver of the software DAMASK is described. The boundary

conditions for the RVE are prescribed in terms of the deformation

gradient 𝐅BC through the following equation:

𝛥𝐅BC =

𝐅−𝐅BC .(6)

DAMASK allows also the definition of mixed boundary conditions to

avoid non-volume preserving loads for very large deformations. For

example a mixed boundary condition for the simulation of tension in

11 direction can be defined through



𝐅BC =⎛⎜⎜⎝

𝑎0 0

0 ∗ 0

0 0 ∗ ⎞⎟⎟⎠

and 𝐏BC =⎛⎜⎜⎝

∗∗∗

∗ 0 ∗

∗ ∗ 0 ⎞⎟⎟⎠

,(7)

where 𝑎is then replaced with a number, which defines the loading rate.

The boundary conditions in Eq. (7) can also be used in combination

with a rotation matrix to define other loading directions. In this work,

𝑎is defined to be 𝑎= 3 ⋅10−4, and the different load situations for

0◦∕45◦∕90◦are realized by the application of rotation matrices.

3.3. Crystal plasticity

For the modeling of material anisotropy, the following CP model

was applied. The deformation gradient is multiplicatively decomposed

in an elastic and plastic part [59]

𝐅=𝐅e⋅𝐅p.(8)

Materials Science & Engineering A 799 (2021) 140154

A. Charmi et al.

Fig. 5. Location of five regions used during EBSD analysis (blue surfaces). Two (3 × 4) mm2EBSD measurements were done on specimens extracted from the middle section of a

Tower 90◦specimen (shown on the left), one (3 × 4) mm2EBSD measurement were done on a specimen extracted from the top section of a Tower 45◦specimen (shown on the

middle) and eight (3 × 4) mm2measurements were done on specimens extracted from one of the walls (shown on the right). (For interpretation of the references to color in this

figure legend, the reader is referred to the web version of this article.)

Fig. 6. RVEs used for CP simulations. (a) 4096 grains, 1 Fourier point per grain, and dimensions of (1120 × 1120 × 1120) μm3, (b) 4096 grains, 64 Fourier points per grain, and

dimensions of (1120 × 1120 × 1120) μm3, and (c) 8000 grains, 1 Fourier point per grain, and dimensions of (1400 × 1400 × 1400) μm3. Note that the colors of the grains do not

represent the grain orientation.

The quantities in the intermediate configuration are marked with an

overbar () and are obtained when the elastic part of deformation is re-

laxed. Therefore, this state of the body represents a reference configura-

tion for the elastic part of the deformation. The second Piola–Kirchhoff

stress 

𝐒can be written as



𝐒=

C∶

𝐄e,(9)

with



𝐄e=1

2((𝐅e)T⋅𝐅e−𝐈)=1

2(

𝐂e−𝐈),(10)

where 

Cis the fourth order tensor of elastic constants, 

𝐂eis the elastic

right Cauchy–Green tensor and 𝐈is the identity tensor. The second

Piola–Kirchhoff stresses are related to the first Piola–Kirchhoff stresses

by 𝐒=𝐏⋅𝐅−𝑇. In case of cubic crystals, the elastic tensor Ccan be

specified with three elastic constants 𝐶11,𝐶12 and 𝐶44. The total power

per unit volume can be decomposed into elastic and plastic parts [60]



𝑤=

𝑤e+

𝑤p=

𝐒∶



𝐄e+ ( 

𝐂e⋅

𝐒) ∶ 

𝐋p,(11)

where 

𝐋pis the plastic velocity gradient in the intermediate configura-

tion, which can be written as a function of dislocation glide on different

slip systems



𝐋p=

𝐅p⋅(𝐅p)−1 =

𝑁

∑

𝛼=1

𝛾𝛼𝐦𝛼

0⊗𝐧𝛼

0,(12)

where 𝐦𝛼

0and 𝐧𝛼

0are unit vectors representing the slip direction and the

normal of the slip plane for the slip system 𝛼, respectively. The plastic

power per unit volume can be calculated using the resolved shear stress

𝜏𝛼and the slip rate 𝛾𝛼



𝑤p=

𝑁

∑

𝛼=1

𝜏𝛼𝛾𝛼,(13)

where 𝑁is the number of slip systems. With the Eqs. (11)–(13) the

resolved shear stress 𝜏𝛼acting on slip system 𝛼reads

𝜏𝛼=

𝐂e⋅

𝐒∶(𝐦𝛼

0⊗𝐧𝛼

0).(14)

The employed phenomenological model in this paper utilizes a rate-

dependent power-law function to define the slip rate 𝛾𝛼[61]

𝛾𝛼=𝛾0|||||

𝜏𝛼

c|||||

𝑛

sgn(𝜏𝛼),(15)

where 𝛾0is the reference shearing rate, 𝑛describes the microscopic

strain rate sensitivity and 𝜏𝛼

cis the slip resistance, which evolves

asymptotically from 𝜏0towards 𝜏∞[58]. Moreover, to incorporate

work-hardening in the material model, the slip resistance 

𝜏𝛼

cis made

to be a function of shear rate



𝜏𝛼

𝑁

∑

𝛽

ℎ𝛼𝛽 𝛾𝛽,(16)

Materials Science & Engineering A 799 (2021) 140154

A. Charmi et al.

Table 2

Single-crystal elastic constants of stainless steel 316L [62].

𝐶11 (GPa)𝐶12 (GPa)𝐶44 (GPa)

206 133 119

Table 3

Results from tensile tests according to DIN EN ISO 6892-1 [39].

0◦45◦90◦

Spec. 1 Spec. 2 Spec. 1 Spec. 2 Spec. 1 Spec. 2

Rp0.2 MPa

Tower 583 583 540 537 500 −−

Wall 581 581 564 563 514 506

Tower 692 692 652 653 619 −−

Wall 689 691 670 671 620 611

Tower 54 55.5 56.5 56.5 60 −−

Wall 56.5 56.5 56.5 53 59.5 53.5

ZTower 72.2 71.3 73.3 71.5 72.2 −−

Wall 73 72.5 71 70.6 72.5 72.3

E GPa Tower 212 218 196 199 198 −−

Wall 213 218 194 210 194 181

where ℎ𝛼𝛽 is the instantaneous strain hardening, which can be calcu-

lated by a saturation-type law [58]

ℎ𝛼𝛽 =ℎ0[𝑞+ (1 − 𝑞)𝛿𝛼𝛽 ]|||1 − 𝜏𝛽

c∕𝜏∞|||

𝑎sgn(1 − 𝜏𝛽

c∕𝜏∞).(17)

The parameters 𝑞,ℎ0,𝜏∞and 𝑎are the latent-hardening, the reference

self-hardening coefficient, saturation value of the slip resistance and the

hardening exponent, respectively. The single-crystal elastic constants

of stainless steel 316L, which are necessary for the calculation of the

elastic tensor C, were taken from [62] and are listed in Table 2.

3.4. Parameter identification

The parameter identification was conducted using a least-squares

based regression analysis. The residual to be minimized by the

Levenberg–Marquardt scheme [63,64] is defined as

minimize (𝐩) = 1

𝑁

∑

𝑖=1

𝑤𝑖(𝑓𝑖(𝐩) − 𝑦𝑖)2,

by changing 𝐩∈𝑆 ,

such that 𝑔𝑗(𝐩)≤0, 𝑗 = 1,…, 𝑛g,

(18)

where is the residual function, 𝑔𝑗is a vector of constraints, 𝐩is a

vector containing the material parameters to be optimized and 𝑤𝑖is

the weight associated to experiment 𝑖. The residual function is the

least-square distance between experiments and simulations. The vector

𝐩contained the parameters 𝑛,ℎ0,𝑎,𝜏0and 𝜏∞. The parameters 𝑞and 𝛾0

were set to a fixed value of 1. During the calibration process only one

tensile test (Tower 45◦) and one EBSD measurement (Tower 45◦) were

used, and the strain range was limited with the lower bound of 0and

upper bound of 0.015. The calibrated parameters were validated using

the remaining experimental data, see Section 4.5 for more details.

4. Results and discussion

4.1. Results from tensile tests and resonance method

The characteristic values for each specimen determined in the ten-

sile tests are listed in Table 3 and the corresponding stress–strain curves

are shown in Fig. 7.

The results reveal that in general, the characteristic strength pa-

rameters (E, Rp0.2 and Rm) increase with decreasing building angle,

and there are no significant differences between specimens from walls

and towers, except for the 45◦orientation, which is considered to be

a result of the rotated scan strategy (see Fig. 1) and will be further

investigated in following sections. The percentage elongation after

Table 4

Results from resonance method according to ASTM E1876 [42].

0◦45◦90◦

Spec. 1 Spec. 2 Spec. 1 Spec. 2 Spec. 1 Spec. 2

E GPa Tower −− −− −− −− −− −−

Wall 225 −− 206 −− 180 −−

fracture (A) and reduction of area (Z) show no dependency on build

orientation. The percentage elongation after fracture (A) is calculated

by carefully fitting back together the broken pieces after fracture and

measuring the gauge length. It should be highlighted that despite the

slight difference between the stress–strain curves for 90◦specimens,

overall, the tensile tests display a low scatter. By comparing the stress–

strain curves, it also becomes clear that each direction has slightly

different yield behavior, characterized by the transition from purely

elastic to plastic deformation. The 0◦direction exhibits the sharpest

transition behavior, whereas the 90◦specimens display a more diffused

transition behavior.

For the resonance method [42] three specimens were cut out from

one of the AM walls with three different inclinations towards the

build plate. The dynamic Young’s moduli were then calculated from

the fundamental flexural resonance frequencies obtained from in-plane

and out-of-plane flexure and were then averaged. The measurement

uncertainty for the dynamic method is around 1%, as previously deter-

mined using other materials by inter-laboratory studies. The measured

dynamic Young’s moduli are listed in Table 4. The results from tensile

tests and the resonance method will be analyzed and compared in detail

in Section 4.4.

4.2. Defects and residual stresses

Six tensile specimens (Tower 0◦, Tower 45◦, Tower 90◦, Wall 0◦,

Wall 45◦and Wall 90◦) were investigated via μCT and neutron diffrac-

tion to detect the microstructural defects and measure the RSs, since

they can have an impact on the material performance of AM parts [27,

65,66]. Table 5 contains the porosity determined for these six tensile

specimens. The segmented pores in all the specimens were spherical.

Therefore, they are expected to be gas pores. As evident from the very

low porosity, it is safe to assume that for the tested specimens in this

paper, the microstructural defects do not contribute to the mechanical

anisotropy and can, therefore, be omitted in the numerical analysis.

The RSs were also determined in six tensile specimens on three

different planes along the height of each specimen. The RSs in normal

direction (Z) of all investigated specimens are shown in Fig. 8. The

highest RS range, from maximum to minimum, of all measured spec-

imens was 142 MPa with an average error of approximately 20 MPa.

The distribution appears not to be symmetric with respect to the

specimen axis. The RS distributions in the specimens 0◦,45◦and

90◦, all three extracted from one wall, are similar. Minor variations

in the RS magnitudes and distributions are considered to be related

to the varying extraction locations and orientations within the wall.

The specimens extracted from individual towers feature similar RS

distributions and magnitudes to the specimens extracted from the wall.

The RS magnitudes are lower for Tower 0◦, possibly resulting from

the increased heat-conducting surface with respect to the low build

height or the employed scan strategy, see Section 2.1. The RSs in Tower

90◦tend to be compressive, which can be a result of an offset for the

stress-free reference, since the RS distribution for this specimen was

acquired during two separate measurements. However, the RS range

and distribution are not influenced by the reference values and are

comparable to the other specimens. The position of the RS profile

dictates the occurrence of compressive or tensile RSs, and it strongly

depends on the stress-free Ref. [67]. The herein determined RS ranges

are low compared to RS ranges of net-shape geometries [50,68,69].

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Fig. 7. Experimentally obtained tensile stress–strain curves. The plots (a, b, c, d) display the same results for different stress and strain ranges, which show that the characteristic

strength parameters increase with decreasing building angle. These results also reveal that the stress–strain curves obtained for the Tower 45◦and Wall 45◦specimens are shifted

relative to each other. This difference in the material behavior is due to the rotated scan strategy, see Fig. 1. Additionally, it should be noted that the difference between the

stress–strain curves for 90◦specimens are not due to a rotation of the scan strategy, since the rotation axis coincides with the loading axis, see Fig. 1. Moreover, the most notable

difference is observed for two of the Wall 90◦specimens (b). After 0.01 strain, the stress–strain curves for a Tower 90◦and a Wall 90◦specimen are nearly identical (b, d). Hence,

for the analysis in subsequent sections, the specimens are grouped in 0◦, Tower 45◦, Wall 45◦and 90◦to account for the effect of the scan strategy.

Table 5

Measured porosity by μCT for six tensile specimens. These results indicate that the anisotropy of LPBF316L specimens is not

affected by the detected gas pores, since the measured porosity is much smaller than 0.01% for all specimens.

Tower 0◦Tower 45◦Tower 90◦Wall 0◦Wall 45◦Wall 90◦

Analyzed volume (mm3) 443.1586 443.7266 442.5135 443.1867 445.1126 444.6265

Volume of pores (mm3) 0.0005 0.0015 0.0009 0.0007 0.0013 0.0010

Number of pores 28 73 42 43 59 57

Porosity <0.01% <0.01% <0.01% <0.01% <0.01% <0.01%

Table 6

Maximum stress range measured in 6 tensile specimens for three orthogonal directions,

see Fig. 4 for the used coordinate system. All values are in MPa.

Tower 0◦Tower 45◦Tower 90◦Wall 0◦Wall 45◦Wall 90◦

Normal direction (Z) 89.98 117.64 142.68 109.5 96.81 107.49

In-plane direction (X) 118.06 84.66 160.78 147.43 106.33 169.34

In-plane direction (Y) 109.3 130.75 149.92 115.31 104.87 159.31

This result can be attributed to mechanical relaxation caused by the ma-

chining of the dogbone geometry of the tensile specimens, as reported

in [49]. Although possible shifts of the RS distribution profile could

occur due to the adopted stress-free reference strategy, the RS ranges

determined within this investigation remain low compared to those

reported for non-machined structures in LPBF316L [50,68,69], see

Table 6. Moreover, it should be highlighted that the tensile specimens

were extracted from walls and towers with different geometries and

thermal histories, which influence the RSs in each specimen. However,

despite the differences in RS profiles, the tensile test results in Fig. 7,

in particular for 0◦direction, are nearly identical. This behavior is a

strong indication that the RSs are not significantly contributing to the

mechanical anisotropy of the tested specimens. Therefore, the RSs are

omitted during the subsequent numerical analysis.

4.3. Texture analysis

In the present study, the texture is determined using EBSD mea-

surements from three different specimens. The measurements were

designed to ensure that the derived crystallographic texture is as rep-

resentative as possible of all the specimens manufactured. Figs. 9–11

contain the EBSD maps, the extracted crystallographic textures, and the

grain size distribution for five different regions with a total scanned

area of 132 mm2. The measurements from the wall (both from side

and cross-section) each consist of four smaller EBSD maps, which are

joined together during post-processing, see Fig. 9(a,b). Note that the

EBSD data were subjected to the smoothing algorithm in the software

MTEX [55,70] to replace the unindexed measurement points. EBSD

maps in Fig. 9 reveal the unusual morphological texture, which is

heavily influenced by the employed scan strategy. The morphological

texture is recognizable as a checkerboard pattern in the cross-section

measurements. Furthermore, the EBSD maps from the side of the spec-

imens display no sign of melt pool boundaries, which is an indication

for epitaxial grain growth of remelted zones. Moreover, the comparison

between the crystallographic texture extracted from the Tower 90◦and

the wall, both from side and cross-section, show a three times random

{110} texture in the build direction, which is in line with the findings

in other studies [13,30,71]. It should be noted that the ODFs extracted

from EBSD measurements are dependent on the measurement frame

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Fig. 8. RSs in the normal direction (Z) measured at different heights. The pictures on the top show RSs in the wall specimens and the pictures on the bottom show RSs in the

tower specimens, both for three inclinations. For the used coordinate system, see Fig. 4. The highest value of measured RS is 137 MPa in Wall 90◦specimen and the lowest value

is −74 MPa in Tower 90◦specimen. However, note that the compressive nature of RSs in Tower 90◦specimen might be due to an offset for the stress-free reference diffraction

values, since the RSs for this specimen were measured during two separate beam times.

and the scan strategy. The ODFs can also be displayed using different

coordinate systems. Changing the measurement frame, the scan strat-

egy, or the coordinate system directly impact the outcome. Hence, all

the ODFs in the pole figures (Fig. 10) are plotted in the same coordinate

system (X, Y, Z)for an easier comparison between the results, see Fig. 1

for all coordinate systems. These five EBSD measurements show that

despite the different geometries, crystallographic and morphological

textures are very comparable in all manufactured specimens.

4.4. Elastic anisotropy

The single-crystal elastic anisotropy of stainless steel 316L can be

described through the elastic tensor C(see Section 3.3), which itself

can be specified with three elastic constants 𝐶11,𝐶12 and 𝐶44. With

these values, it is possible to calculate and predict the anisotropic

elastic behavior in any direction. However, this is only applicable to a

specimen containing a single grain, since these values are only correct

for a single-crystal with a certain crystallographic orientation. The

LPBF316L specimens tested in this paper are polycrystalline, as evident

from the EBSD measurements, see Fig. 9, and the macroscopic elastic

behavior of a polycrystalline specimen is determined by the average

behavior of its grains and heavily influenced by the crystallographic

texture.

To analyze the macroscopic elastic anisotropy of LPBF316L the

Young’s moduli were experimentally measured using both tensile test-

ing and resonance method. The Young’s moduli, which were deter-

mined from eleven tensile tests (see Table 3), were averaged for loading

directions 0◦, Wall 45◦, Tower 45◦and 90◦and measured to be 215 ±

3GPa, 202 ± 8 GPa, 198 ± 2 GPa and 192 ± 7 GPa, respectively. The

results for Wall 45◦and Tower 45◦specimens are averaged separately to

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Fig. 9. EBSD measurements from cross-section of wall (a), side of wall (b), cross-section of Tower 90◦(c), side of Tower 90◦(d) and side of Tower 45◦(e). Note that the coordinate

systems (X, Y, Z)and (X′,Y′,Z′)are different, for more details see Fig. 1. The corresponding pole figures are shown in Fig. 10.

account for the influence of the rotated scan strategy during specimen

production, see Figs. 1 and 7. The measured dynamic Young’s moduli

for Wall 0◦, Wall 45◦and Wall 90◦specimens are 225 GPa, 206 GPa and

180 GPa, respectively.

The macroscopic elastic anisotropy was numerically estimated for

all tested directions using the softwares DAMASK [57] and MTEX [55].

The details of the CP model implemented in DAMASK are explained in

Section 3.3. The software MTEX has three built-in methods (Voigt, Hill,

Reuss) for the estimation of the macroscopic elastic behavior. For the

sake of brevity, the reader is referred to [70] for specifics about these

methods and the usage of the software MTEX.

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Fig. 10. Pole figures from cross-section of wall (a), side of wall (b), cross-section of Tower 90◦(c), side of Tower 90◦(d) and side of Tower 45◦(e). Note that for an easier

comparison, all pole figures (a, b, c, d, e) are shown in the same coordinate system (X, Y, Z)and not the coordinate system of their corresponding EBSD map in Fig. 9. It is

evident from the results that all specimens have a very similar {110} texture in the build direction.

Fig. 11. Grain size distributions determined from five EBSD measurements, see Fig. 9. The grain size is calculated from the grain area assuming a rectangular grain shape. The

kernel density estimation (KDE) visible in the plot is the average KDE of all five grain size distributions.

For the numerical analysis, the extracted crystallographic textures

from all five EBSD measurements and the single-crystal elastic con-

stants of stainless steel 316L from [62] were used, which are listed in

Table 2. The experimental and numerical results, which are displayed

in Fig. 12, reveal that the Hill estimation approach [70] and the crystal

plasticity model are capable of predicting the elastic anisotropy. The

numerical results for each estimation method displayed in different

colors cover the range between the minimum and maximum value

obtained for all five crystallographic textures as slight variations in

ODFs influence the numerical results. Furthermore, it should be noted

that the observed differences between the results from tensile tests and

resonance method might be due to measurement inaccuracies since the

employed extensometer for the tensile tests was calibrated in the range

of −10% to 50% percent strain and is therefore not perfectly suited

for precise measurements of Young’s moduli. However, despite these

differences, it can be argued that for the tested specimens in this paper,

the crystallographic texture is responsible for the elastic anisotropy

since the directional dependency of the Young’s moduli was captured

by only using the crystallographic texture and single-crystal elastic

constants as inputs for the simulations softwares. These results are

also in line with the findings in [72,73], which showed experimentally

and numerically that the elastic anisotropy of their AM inconel 718

specimens were well reflected by the crystallographic texture.

4.5. Anisotropic yield behavior

The tensile test results revealed both the elastic anisotropy and also

the anisotropic yield behavior of the LPBF316L specimens, see Figs. 7

and 12. In the last section, it was shown that the elastic anisotropy

of the tested specimens is highly correlated with the crystallographic

texture. The CP model was calibrated using only the tensile test results

for the Tower 45◦and the EBSD measurement from the side of Tower

45◦specimen, see Figs. 7 and 9. The calibration process was done with

only a single tensile test and one EBSD measurement to demonstrate

the efficiency and reliability of the numerical method. Moreover, the

CP model can be calibrated using any of the tensile test results and

EBSD measurements. The strain range for the calibration process was

between 0and 0.015. The calibrated parameters of the CP model are

listed in Table 7.

The remaining tensile test results and EBSD measurements were

used for the validation and sensitivity analysis of the model. The

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Fig. 12. Comparison between experimentally measured and numerically estimated Young’s moduli using softwares MTEX (a) and DAMASK (b). Each color, which corresponds to

a different estimation method, renders the range between the minimum and maximum value obtained for five separate extracted crystallographic textures, see Fig. 10.

Fig. 13. Comparison between experimental and numerical results (CP) in the strain range of 0.002 to 0.015. The lines represent the experimental stress–strain curves. The plots

(a, b, c, d) each contain the simulation results for one specific loading direction. The results for Tower 45◦(b) and Wall 45◦(c) specimens are displayed separately to account

for the influence of the rotated scan strategy during specimen production. The rotation of the scan strategy does not influence the results for the 90◦(a) specimens, since the

rotation axis coincides with the loading axis, see Figs. 1 and 7for more details. The simulation results cover the range between minimum and maximum value obtained for all

five extracted crystallographic textures, see Fig. 9.

experimental and simulated true stress–strain behaviors for all loading

directions and crystallographic textures are plotted in Figs. 13 and 14.

The numerical results for each loading direction displayed in different

colors cover the range between the minimum and maximum value ob-

tained for all five experimentally determined crystallographic textures,

see Fig. 10. As evident in Fig. 7 the tensile test results for each loading

direction are very similar. Hence, for easier comparison between the

stress–strain curves, only one single tensile test result is plotted for

each loading direction. These results show an overall good agreement

between the experiments and model prediction.

The maximum deviations between the simulations and experiments

are displayed in Fig. 15 as %-error, which demonstrates the accuracy

of the numerical model. The %-error is below 5% after only 0.004

strain and stays under 3% after 0.025 strain. These variations are

tolerable considering the different sources of measurement error, such

as the difficulties of extracting the crystallographic texture from a 2D

surface area. Different aspects like surface finish, beam shift, and tex-

ture gradients in the material influence the result. Moreover, it should

be highlighted that after the model calibration, the same parameter

set was used for running all other simulations. This means that the

simulation results for textures extracted from the four remaining EBSD

measurements can be further optimized since they were not used during

the calibration process. However, the main goal of this paper is to

demonstrate the sensitivity and reliability of this approach.

Furthermore, it is evident from Fig. 13 that there is a variation in

the yield behavior for each loading direction which leads to a greater

Materials Science & Engineering A 799 (2021) 140154

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Fig. 14. Experimental and numerical results for all extracted crystallographic textures displayed in the strain range of 0.005 to 0.16, which demonstrate the accuracy of the CP

model outside of its calibration range. Note that the strain range for the calibration process was between 0and 0.015, see Fig. 13.

Fig. 15. Maximum deviation between the experimental and numerical stress–strain curves (Figs. 13 and 14) presented as %-Error.

deviation between the simulations and experiments, most notably at

the beginning of yielding. This behavior might be explained through

different competing deformation mechanisms for each particular load-

ing direction. Nano twinning is sometimes the dominating deformation

mechanism, as reported in related studies [13,17,19,31]. However, in

the currently used CP model only dislocation slip is taken into account.

Concluding the findings in this section, the results strongly indicate

that the crystallographic texture is the main contributing factor to

the anisotropy of LPBF316L, since the CP model was able to accu-

rately capture and predict the anisotropic yield behavior of the tested

specimens.

The findings in this section are based on a micro-mechanical crystal

plasticity model. Due to the high computational cost, such models can

usually only realistically simulate the deformation behavior in small

regions, such as the representative volume elements (RVEs) employed

in this work. However, additively manufactured parts are orders of

magnitude larger than these RVEs. To overcome this constraint, dif-

ferent methods were developed [58,74], which allow these results

to be transferred to the macro-scale. For example, in a virtual-lab

framework [58], the calibrated crystal plasticity model can be used to

simulate the yield behavior for many different loading conditions. The

results of the simulations can in turn be used to calibrate a macroscopic

yield surface and thus, allow the use of finite element softwares for

simulating the deformation behavior of additively manufactured parts

with complex geometries. On a final note, although it is possible to

simulate any desired stress state with a calibrated crystal plasticity

model, more experimental validation is recommended to ensure the

best possible results when simulating complex loading paths. This can

be achieved for example using notched specimens or doing shear or

torsion tests.

5. Conclusions

The mechanical anisotropy of LPBF316L was investigated using

both experimental and numerical methods to determine the underlying

origin. Several important aspects were examined to isolate the main

Materials Science & Engineering A 799 (2021) 140154

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Table 7

Calibrated material parameters of the CP model.

𝛾0(1/s)𝑛 ℎ0(MPa)𝑎 𝜏0(MPa)𝜏∞(MPa)

1 38 3160 9 263 1130

contributing factor, since the origin of anisotropy in LPBF316L in liter-

ature remains inconclusive and exhibits a broad range of explanations.

1. The mechanical testing showed that the yield strength increased

with decreasing angle of the building direction relative to the

build plate for all tested specimens.

2. EBSD analysis revealed a preferential ⟨110⟩orientation parallel

to the build direction and a checkerboard morphology, which

were a direct result of the layerwise 90◦rotation of the scan

strategy and were in line with the findings in other studies.

3. The measured porosity in all specimens was much smaller than

0.01%, and the detected defects were spherical. Despite the dif-

ferences in measured RS profiles, the tensile stress–strain curves

for certain loading directions were nearly identical. With these

findings, it was concluded that contrary to the statements in

some publications, the anisotropy of the tested specimens in this

paper is not predominantly controlled by either defects or RSs.

4. Elastic anisotropy was experimentally determined using both

tensile testing and resonance method. Through numerical anal-

ysis, it was shown that the elastic anisotropy was dominated by

crystallographic texture.

5. The anisotropic yield behavior of LPBF316L was modeled using

a CP model. The numerical investigations strongly indicated that

the directional dependency of yield behavior is mainly governed

by the crystallographic texture.

Overall, it can be concluded that the crystallographic texture is the

main contributing factor to the mechanical anisotropy of the tested

LPBF316L specimens. Moreover, the approach presented in this paper

can be employed to accurately capture and predict the mechanical

anisotropy of AM specimens in an efficient manner, since it only

requires a single tensile test and one EBSD measurement.

Funding

The funding of BAM Focus Area Project AGIL, Germany is acknowl-

edged.

CRediT authorship contribution statement

A. Charmi: Conceptualization, Methodology, Formal analysis, Vi-

sualization, Validation, Writing - original draft, Writing - review &

editing. R. Falkenberg: Conceptualization, Supervision, Writing - origi-

nal draft, Writing - review & editing. L. Ávila: Investigation, Resources,

Data curation, Writing - original draft, Writing - review & editing. G.

Mohr: Investigation, Resources, Writing - original draft, Writing - re-

view & editing. K. Sommer: Investigation, Formal analysis, Resources,

Writing - original draft, Writing - review & editing. A. Ulbricht: Inves-

tigation, Resources, Formal analysis, Writing - original draft, Writing

- review & editing. M. Sprengel: Investigation, Resources, Formal

analysis, Writing - original draft, Writing - review & editing. R. Saliwan

Neumann: Investigation, Formal analysis, Resources, Writing - original

draft, Writing - review & editing. B. Skrotzki: Project administration,

Supervision, Funding acquisition, Writing - review & editing. A. Evans:

Investigation, Project administration, Writing - original draft, Writing -

review & editing.

Declaration of competing interest

The authors declare that they have no known competing finan-

cial interests or personal relationships that could have appeared to

influence the work reported in this paper.

Data availability

The raw/processed data required to reproduce these findings cannot

be shared at this time as the data also forms part of an ongoing study.

Acknowledgment

Robert Wimpory of the HZB is acknowledged for support of the

residual stress measurements on the E3 diffractometer.

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