Characterization and Simulation of Shear-Induced Damage in Selective-Laser-Sintered Polyamide 12

Abstract

This paper presents the characterisation of selective-laser-sintered (SLS) samples of polyamide 12 (PA12) under shear loading. PA12 is a semi-crystalline thermoplastic and is used in various industries. Its behaviour under shear stress, which is particularly important for product reliability, has not yet been sufficiently investigated. This research focuses on understanding the material and damage behaviour of PA12 under shear-induced stress conditions. The study included quasi-static experiments and numerical simulations. Samples were prepared via SLS and tested according to ASTM standards. Digital image correlation (DIC) was used for precise deformation measurements. The Chaboche material model was used for the viscoplastic behaviour in the numerical simulations. Due to existing material discontinuities in the form of voids, the material model was coupled with the Gurson–Tvergaard–Needleman (GTN) damage model. A modified approach of the GTN model was used to account for low stress triaxiality under shear loading. These models were implemented in MATLAB and integrated into Abaqus via a User Material (UMAT) subroutine. The results of the experiments and simulations showed a high degree of accuracy. An important finding was the significant influence of the shear factor kw on the damage behaviour, especially during failure. This factor proved to be essential for the accurate prediction of material behaviour under shear-induced stress conditions. The integration of the modified GTN model with the Chaboche material model in UMAT enables an accurate prediction of the material and damage behaviour and thus makes an important contribution to the understanding of the mechanical material behaviour of SLS PA12 specimens.

Full text

Citation: Schob, D.; Richter, L.;
Kotecki, K.; Kurpisz, D.; Roszak, R.;
Maasch, P.; Ziegenhorn, M.
Characterization and Simulation of
Shear-Induced Damage in
Selective-Laser-Sintered Polyamide 12.
Materials 2024,17, 38. https://
doi.org/10.3390/ma17010038
Academic Editors: Constantinos
Simserides, Laurence G. D. Hawke
and Petra Baˇcová
Received: 21 November 2023
Revised: 14 December 2023
Accepted: 18 December 2023
Published: 21 December 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
materials
Article
Characterization and Simulation of Shear-Induced Damage in
Selective-Laser-Sintered Polyamide 12
Daniela Schob 1,* , Lukas Richter 1, Krzysztof Kotecki 2, Dariusz Kurpisz 2, Robert Roszak 1,2,* ,
Philipp Maasch 1and Matthias Ziegenhorn 1
1Chair of Engineering Mechanics and Machine Dynamics, Faculty of Mechanical Engineering, Electrical and
Energy Systems, Brandenburg University of Technology Cottbus-Senftenberg, 01968 Senftenberg, Germany;
matthias.ziegenhorn@b-tu.de (M.Z.)
2Institute of Applied Mechanics, Poznan University of Technology, 60-965 Poznan, Poland
*Correspondence: daniela.schob@b-tu.de (D.S.); robert.roszak@put.poznan.pl (R.R.)
Abstract: This paper presents the characterisation of selective-laser-sintered (SLS) samples of polyamide
12 (PA12) under shear loading. PA12 is a semi-crystalline thermoplastic and is used in various
industries. Its behaviour under shear stress, which is particularly important for product reliability,
has not yet been sufficiently investigated. This research focuses on understanding the material and
damage behaviour of PA12 under shear-induced stress conditions. The study included quasi-static
experiments and numerical simulations. Samples were prepared via SLS and tested according to
ASTM standards. Digital image correlation (DIC) was used for precise deformation measurements.
The Chaboche material model was used for the viscoplastic behaviour in the numerical simulations.
Due to existing material discontinuities in the form of voids, the material model was coupled with
the Gurson–Tvergaard–Needleman (GTN) damage model. A modified approach of the GTN model
was used to account for low stress triaxiality under shear loading. These models were implemented
in MATLAB and integrated into Abaqus via a User Material (UMAT) subroutine. The results of
the experiments and simulations showed a high degree of accuracy. An important finding was
the significant influence of the shear factor
kw
on the damage behaviour, especially during failure.
This factor proved to be essential for the accurate prediction of material behaviour under shear-
induced stress conditions. The integration of the modified GTN model with the Chaboche material
model in UMAT enables an accurate prediction of the material and damage behaviour and thus
makes an important contribution to the understanding of the mechanical material behaviour of SLS
PA12 specimens.
Keywords: selective-laser-sintered polyamide 12 (PA12); shear loading; user material routine (UMAT);
Chaboche model; GTN model; viscoplasticity
1. Introduction
The advancement of technology necessitates the creation of innovative materials.
Polymers are becoming increasingly important as a construction material with additive
manufacturing (AM) methods being utilised. By using AM technology, a digital computer-
aided design (CAD) is converted into real objects, enabling a rapid transition from design
to end product. This is achieved by building up the objects layer by layer, without the
need for moulding or mechanical processing [
1
]. During their service life, 3D-printed parts
produced in this way must be able to withstand various mechanical loads. Knowing the
required strength under different loads is essential [
1
,
2
]. A frequently used AM process for
polymers is powder bed sintering, also known as SLS [
3
]. In this process, one or more lasers
selectively fuse powder particles on the surface, layer by layer [
4
–
6
]. PA12 is one of the most
commonly used materials for the SLS process. This semi-crystalline thermoplastic is ideal
for functional prototypes or end-use parts due to its mechanical properties, flexibility, and
Materials 2024,17, 38. https://doi.org/10.3390/ma17010038 https://www.mdpi.com/journal/materials

Materials 2024,17, 38 2 of 15
heat resistance [
3
,
7
,
8
]. The adaptability of SLS PA12 is demonstrated by its successful inte-
gration in a wide range of industries, from the manufacture of high-performance ball valves
and medical devices to customised automotive parts and beyond [
3
,
9
–
13
]. In order to utilise
the full potential of SLS PA12, a thorough understanding of the material properties under
a wide range of loading conditions is essential. In recent years, studies have been conducted
on the material behaviour of SLS PA12 under both quasi-static and cyclic loading [
14
–
18
].
Due to the lack of comprehensive standards in the field of AM, the procurement and
interpretation of material data remain difficult [
19
]. One particular area to be investigated is
the behaviour of SLS PA12 under shear-induced stress conditions, an area that is relatively
under-researched [
20
–
22
]. The challenge is not only to identify the details of the material
behaviour, but also to determine the most suitable test geometries that can provide reliable
and reproducible results, especially in shear-dominated
scenarios [23–26].
Even though
the current state of the art in SLS is advanced, it also has its limitations. The process can
lead to structural inhomogeneities in the final product in the form of voids, microcracks,
or even unsintered areas [
16
,
27
–
30
]. These microstructural features in combination with
the described complex material properties pose challenges for numerical modelling. In
the work of [
15
,
16
], the material model of Chaboche [
31
] was coupled with the damage
model of Gurson–Tvergaard–Needleman [
32
], and a high accuracy between experiment
and simulation was achieved. The GTN model does not take shear stress into account.
In this respect, attempts have been made in recent years to modify this model, following
the work of Xue [
33
] and Nahshon and Hutchinson [
34
], who presented a framework that
potentially provides higher accuracy under combined tensile and shear loading.
The present work has three objectives. The first one is the experimental characterisation
of the material and damage behaviour of SLS PA12 under shear load. The second aim of
the study is to couple Chaboche’s material model with the modified GTN damage model
based on Nahshon and Hutschinson’s approach to ensure that it captures the details of
shear-induced behaviour with optimal precision. Due to the limited data available for SLS
PA12 in common FE software (ABAQUS 2022) material libraries, the third objective of this
work is to implement the material and damage model in a UMAT.
2. Experiments
2.1. Sample Preparation
The specimens were fabricated utilizing SLS technique. A PA2200 powder was de-
ployed for the process. A sPro 230 3D printer, manufactured by 3D Systems and functioning
at a power output of 70 W, was utilized in the fabrication. The printer operated at a laser
scanning speed of 10 m/s for the infill and 5 m/s for the contour delineation. The nominal
layer thickness was maintained in the range of 0.08 to 0.15 mm. The process and the cham-
ber temperature during the print cycle were sustained at 200 °C and 170 °C, respectively.
Given the current lack of standardized testing procedures for AM polymers under
shear loading [
19
], the testing geometry was chosen in line with the ASTM B831 stan-
dard [
35
], as illustrated in Figure 1a. Based on prior research, it has been observed that
the resultant material properties demonstrate only minimal dependence on the printing
direction [
15
]. Therefore, all subsequent tests were performed on specimens layered along
the z-axis, Figure 1b.
2.2. Digital Image Correlation
For the execution of DIC, the ARAMIS 3D Camera measurement system was deployed
for comprehensive area-based and discrete point measurements. DIC is an optical non-
contact method, allowing for full-field measurement of deformations. The technique relies
on a reference image to serve as a baseline for deformation measurements. Consequently,
a unique binary (black and white) pattern is applied to the specimen surface (Figure 1c).
These stochastic patterns facilitate the identification of discrete image areas, with subpixel
accuracy, through the analysis of image-based information, Figure 2.

Materials 2024,17, 38 3 of 15
Figure 1. ASTM shear specimen: (a) geometry, (b) single printing layers are in the xy-plane, the
build-up direction of the layers is the z-direction; and (c) black and white pattern for DIC.
The methodology generates point and area measurement results which are subse-
quently used in material research and component testing to evaluate the static behaviour of
specimens [36]. The fundamental correlation function is represented as [37]:
C(x,y,u,v) =
N/2
∑
i,j=−N/2
(I(x+i,y+j)−I∗(x+u+i,y+v+j))2(1)
where
C
is a function of the coordinates xand yof the reference image. The displacement
and disparity are defined as
u
and
v
, respectively.
I
represents the pre-deformation image
and is a function of the pixel values
x+i
and
y+j
. The post-correlation,
I∗
, signifies the
image function of the pixel values after the application of displacements.
The function
C(x
,
y
,
u
,
v)
represents the cumulative squared differences between the
reference and the deformed images, where the function is summed over the subset size
N
.
Figure 2. Reference image of DIC in Aramis.
Using the Hegewald & Peschke Inspekt-Table 10 kN testing machine (Nossen, Ger-
many), five shear tests were conducted at a 1 mm/min displacement rate and a temperature
of 23 °C.
3. Numerical Simulation
3.1. Chaboche Model
Previous investigations have shown that SLS PA12 behaves viscoplastically [
15
]. This
study focuses on the development of material-specific adjustments of the Chaboche material
model, with limitations set on purely isothermal conditions. The Chaboche model is

Materials 2024,17, 38 4 of 15
constituted of a system of differential equations, originating from the division of the total
strain rate ˙
εtot into an elastic ˙
εel and a viscoplastic ˙
εvp component [38]:
˙εtot =˙εel +˙εv p, (2)
˙
σ=E:˙εtot −˙εv p, (3)
with the stress
σ
and Young’s Modulus
E
. Herein, the definition of the viscoplastic strain
rate ˙εvp , composed of the viscoplastic multiplier ˙
λand the direction ∂f/∂σ, is decisive:
˙εvp =˙
λ∂f
∂σ=f
Kn ∂f
∂βv
∂βv
∂σ+∂f
∂βH
∂βH
∂σ!. (4)
The index (
·
)
v
indicates that it is an equivalent stress and (
·
)
H
hydrostatic stress. The
relative stress βis defined by [39]
β=σ−(1−ˆ
f)
2
∑
k=1
Xk, with k=1, 2. (5)
The flow function
f
delineates the closure of the elastic domain and
Xk
the non-linear
kinematic hardening. Equation
(6)
defines the flow function of viscoplastic behaviour [
32
]:
f=βv
σM2
−1+2q1ˆ
f∗cosh 3q2
2
βH
σM!−(q1ˆ
f∗)2≥0. (6)
The parameters
q1
and
q2
are damage parameters and
ˆ
f∗
is the void volume fraction.
The flow function is dependent on the non-linear isotropic hardening σM[38]:
σM=σy+Q∞(1−ex p(−b¯
εvp )) +K(˙
¯
εvp )1/n, (7)
with the accumulated plastic strain rate
¯
εvp
, where its derivative is the modulus of plastic
strain rate:
˙
¯
εvp =σ: ˙εv p
1−ˆ
f∗σM. (8)
The isotropic hardening
σM
describes the extension of the flow surface and is defined
by the yield stress
σy
, the viscosity factor
K
, the viscosity exponent
n
, and the hardening
parameters
Q∞
and
b
. In addition to the isotropic hardening, the flow function is influenced
by the non-linear kinematic hardening
X
. The kinematic hardening depends on the strain
hardening parameter
C
, the dynamic recovery factor
γ
, the static recovery factor
Rkin
,
the decay constant
ω
, and the saturation parameter
φ∞
. The first term in Equation
(9)
describes the strain hardening and the second and third ones describe the dynamic and
static recovery, respectively [40]:
˙
X=
2
∑
i=12
3C(i)˙εvp −γ(i)φ(i)X(i)˙
¯
εvp −Rkin(i)X(i), (9)
with:
φ=
2
∑
i=1φ(i)
∞+ (1−φ(i)
∞)exp(−ω(i)¯
εvp ). (10)
3.2. GTN Damage Model
The results of the micromechanical analysis from a previous investigation [
15
] were
taken into account for the selection of the damage model. The virgin samples have a large
portion of nearly spherical voids. Due to the quasi-static and cyclic loading, the voids are
growing. When the spaces between the voids become small enough coalescence occurs.

Materials 2024,17, 38 5 of 15
This coalescence needs to be embedded in the GTN model [
32
] so that it takes into account
pore growth, nucleation, and coalescence.
In Equation
(11)
, the effective void volume fraction
f∗
is presented. This models the
correlation between the reduction in the material’s load-bearing ability and coalescence [
41
].
ˆ
f∗=








ˆ
f0if t0=0
ˆ
fif ˆ
f≤ˆ
fc
ˆ
fc+
1
q1−ˆ
fc
ˆ
fF−ˆ
fc(ˆ
f−ˆ
fc)if ˆ
fc<ˆ
f≤ˆ
fF.
(11)
The initial porosity,
ˆ
f0
, is set at
t=
0. As the void volume approaches the critical limit
ˆ
fc
, coalescence begins. This continues until the material reaches the failure void volume
fraction
ˆ
fF
and subsequently fails. To describe the void volume fraction
ˆ
f
, modifications
were made to the original GTN model. Nahshon and Hutchinson’s [
34
] approach was
utilized, which considers the impact of shear load on damage behaviour. As a result, the
shear term ˆ
fShear was added [34]:
ˆ
f=ˆ
f0+˙
ˆ
fShear +˙
ˆ
fGrowth +˙
ˆ
fNucleation dt, (12)
so the void volume fraction
ˆ
f
, is characterized by the sum of the initial void volume
ˆ
f0
, void
growth
ˆ
fGrowth
, void nucleation
ˆ
fnucl eati on
, and void volume fraction due to shear
ˆ
fShear
.
The increment in the void volume fraction due to pore growth
˙
ˆ
fGrowth
is described by the
effective void volume fraction ˆ
f∗and the viscoplastic strain rate ˙
εvp [32]:
˙
ˆ
fGrowth = (1−ˆ
f∗)Sp(˙εvp). (13)
Assuming a strain-controlled load, the nucleation of pores follows a normal Gaussian
distribution. This has a mean value
εN
and a standard deviation
SN
. The new pore
volume created via nucleation corresponds to the parameter
ˆ
fN
. The nucleation is strongly
dependent on the matrix material [32]:
˙
ˆ
fNucleation =ˆ
fN˙
εvp
SN√2πex p −1
2εvp −εN
SN2!. (14)
Nahshon and Hutchinson formulated an equation to predict the increase in void
volume fraction at low stress triaxiality, expressed as follows [34]:
ˆ
fshear =kw
ˆ
f∗·w(σ)
σvS:˙εvp , (15)
with the shear factor kω, the deviatoric stress tensor S, and the stress state function [34],
w(σ) = 1−27J3
2(σv)32
, (16)
with the third invariant of the deviatoric stress tensor J3=|S|.
All the described parameters of Equations
(2)
–
(16)
were adjusted using the pattern
search algorithm [
42
] and subsequently incorporated into Abaqus for the execution of the
numerical simulation.
3.3. UMAT in Abaqus
Initially, the coupled Chaboche-GTN model was implemented in Matlab for one point.
The return mapping algorithm is an iterative method used in plasticity theory [
43
,
44
]. For
each incremental step of the simulation, an elastic prediction is made first. Then, it is
checked whether the resulting stress meets the yield condition. If the yield condition has

Materials 2024,17, 38 6 of 15
been reached, it is assumed that a plastic deformation has occurred and a correction must be
made. This correction, namely the determination of the corresponding plastic deformation
increment to “return” the stress to the yield surface, is performed by the return mapping
algorithm [43].
The model parameters of the coupled Chaboche-GTN model were determined using
a pattern search algorithm [
42
] in MATLAB together with the experimental data from the
shear tests. This process ensured that the simulation results accurately reflected the actual
experimental results. The main goal of applying the pattern search algorithm was to fit
the model as closely as possible to the actual physical phenomena in order to improve its
accuracy and reliability. This step is crucial for validating the effectiveness of the model
and its ability to accurately replicate real physical processes. Table 1lists the parameters
determined. The modulus of elasticity
E
, the yield stress
σy
, the initial void volume
fraction
ˆ
f0
, and the void volume fraction at failure
ˆ
fF
were determined directly from the
experiments. All other parameters were determined by optimisation.
Table 1. Determined parameters.
Parameter Unit Value
Poisson ratio ν4.13
Young’s modulus EMPa 1203.00
Yield stress σyMPa 8.00
Viscosity factor KMPa 11
Viscosity exponent n2.7
Hardening parameter C1MPa 593.7
Hardening parameter C2MPa 457.97
Recovery factor γ1138.97
Recovery factor γ2126.50
Hardening parameter Q∞126.50
Hardening parameter b28.65
Static recovery factor Rkin(1)0
Static recovery factor Rkin(2)0
Saturation parameter φ1
∞0
Saturation parameter φ2
∞0
Decay constant ω10
Decay constant ω10
Initial void volume fraction ˆ
f00.0435
Damage parameter q10.7
Damage parameter q20.5
Failure void volume fraction ˆ
fF0.052
Nucleation void volume fraction ˆ
fN1.4 ×10−4
Mean value εN0.0173
Standard deviation SN0.1536
Void volume fraction coalescence ˆ
fC0.0438
Shear factor kw0.12
For the integration of the model into the finite element analysis software Abaqus
2022, the UMAT function was utilized. UMAT is a subroutine within Abaqus 2022 that
allows users to define and implement custom material models in FORTRAN. This function
provides the flexibility to model complex material behaviours that go beyond the models
typically provided in Abaqus. A schematic overview of the process flow and the implemen-
tation of the applied model is depicted in Figure 3. The parameters derived from Matlab
were used as input variables for the finite element analysis.

Materials 2024,17, 38 7 of 15
Figure 3. UMAT scheme.
For the finite element simulation, a reference model for the “simple shear” load case
was created to cross-check the results of the UMAT in MATLAB. The C3D8 element was
chosen for this purpose, a three-dimensional element with eight nodes and a linear shape
function. With the support of constraints and the “Equations” function, these points were
linked to the respective surfaces. Specifically, RP-1 was associated with the displayed
surface III in the x-direction, and RP-2 in the y-direction for surface I. In the load case,
the movement of RP-1 and its associated surface was fixed in the x-direction, while RP-2
underwent a defined displacement in the y-direction. For surface VI, the displacement in
both the z and y directions was set to zero. Similarly, for surface IV, the displacement in the
x and z directions was also set to zero. To simulate “simple shear”, two reference points,
RP-1 and RP-2, were introduced, as shown in Figure 4a.
(a) (b) (c)
Figure 4. (a) Boundary condition simple shear model (b), mesh of half model, (c) boundary condition
of the half model.

Materials 2024,17, 38 8 of 15
In addition to the reference model, a half-model of the original geometry was used, as
shown in Figure 1. This half-model is depicted in Figure 4b. The boundary conditions are
defined as follows: The displacement is constrained in the x-direction on Surface I, in the
y-direction on Surface IV, and in the z-direction on Surface V, Figure 4c. A displacement
in the y-direction is prescribed on Surface III. For this model, the C3D8 element type
was taken.
4. Results and Discussion
4.1. Experimental Results
The results of the five experiments are visualised in the shear stress–time diagram in
Figure 5.
Figure 5. Experimental results of shear stress over time.
The mean value
¯
x
of the shear modulus and ultimate strength determined from these
five shear tests and the corresponding standard deviations sare listed in detail in Table 2.
¯
x=1
n
n
∑
i=1
xis=s1
n
n
∑
i=1
(xi−¯
x)(17)
Table 2. Mean values and standard deviation.
Unit Mean Value Standard Deviation
Shear modulus MPa 667.37 10.34
Ultimate strength MPa 32.22 2.51
The standard deviation values, 10.34 MPa for shear modulus and 2.51 MPa for ultimate
strength, suggest a consistent performance of the material across different samples. Test 4
was used for the further fitting of the model parameters.
4.2. Simulation Results
Prior to the analysis, a thorough verification process was conducted to ensure the
integrity of the transferred code from MATLAB to UMAT. After reviewing the model in
MATLAB and integrating it into the UMAT, the FE model for simple shear (Figure 4) was
analysed. In Figure 6, the deformed body and the associated shear stress σ12 are depicted.

Materials 2024,17, 38 9 of 15
Figure 6. Shear stress.
A strong correlation was observed between the results from MATLAB (red line) and
the UMAT (green dotted line) in comparison to the experimental data (black line), Figure 7.
Both the material behaviour and the time of failure could be simulated exactly.
Figure 7. Shear stress over strain.
As expected, an increased shear stress
σ12
was observed in the region of the webs
(Figure 8).

Materials 2024,17, 38 10 of 15
Figure 8. Stress field σ12.
The analysis of the shear stress
σ12
at a node (black point) in the shear zone and
its comparison to the experiment are illustrated in Figure 9. The material and damage
behaviour can be mapped with a very high accuracy. The maximum deviation is 1 MPa
and occurs at the point in time when the shear and tensile loads superimpose each other.
Figure 9. Shear stress over time of the node of full model.
Furthermore, the influence of the newly introduced shear factor
kw
(Equation
(15)
)
was examined (Figure 10a). The value for
kw
determined through optimization is 0.12
(Figure 10a, dotted red line). To analyse its influence, this value was increased to 0.18 and
decreased to 0. The results are depicted in the stress–time diagram, both throughout the
entire course (Figure 10a) and in detail shortly before failure (Figure 10b).

Materials 2024,17, 38 11 of 15
(a) (b)
Figure 10. (a) Shear stress full model of UMAT and (b) cutout of stress–time curve under the influence
of kw.
From Figure 10b, it becomes evident that
kw
has a significant influence on the char-
acterization of the damage behaviour, especially shortly before failure. When the value
of
kw
decreased, the stress is overestimated, while it is underestimated when increased.
Misestimating this value can lead to inaccurate stress and failure predictions. Therefore,
it is essential to calibrate
kw
correctly to ensure that model predictions align with the real
damage behaviour.
In order to investigate whether pure shear or a superposition of shear and tension is
present in the component, the calculation of the stress triaxiality η,
η=−σH
σv, (18)
provides a statement [
45
,
46
]. The stress triaxiality indicates the ratio of hydrostatic stress
σH
to the Mises equivalent stress
σv
. A high value of the stress triaxiality
η=
0.33 indicates
that pure tensile or compressive stress predominates. Low values indicate pure shear stress.
Figure 11 illustrates the stress triaxiality in the same node as the analysis of the shear stress
(Figure 8). At the beginning of the loading, there is pure shear stress. As the load progresses,
the stress triaxiality increases to a value of
η=
0.17 and a combination of shear and tensile
stresses occurs, with shear stress remaining the predominant factor. The results presented
in Figure 9demonstrate that the enhanced GTN model is capable of accurately representing
both pure shear stresses and the combined loading scenario of shear and tension.
Figure 11. Stress triaxiality of full model of UMAT.

Materials 2024,17, 38 12 of 15
The programmed material and damage model in UMAT allows for the representation
of individual development variables. In Figure 12, the void volume fraction at the time
t=
40 s is depicted as
ˆ
f∗
. The complete progression of the void volume fraction over time
is shown in Figure 12. Until the yield point is reached, the void volume fraction retains its
initial value
ˆ
f0
. As soon as the yield point is exceeded, the void volume fraction gradually
increases. When the coalescence threshold
ˆ
fc
is reached, the increase in the void volume
fraction accelerates significantly.
(a) (b)
Figure 12. (a) Void volume fraction of full model of UMAT,
t=
40 s and (b) development of void
volume fraction over time.
In Figure 13, the results from Abaqus and the DIC are compared. The focus is on the
comparison of the deformation fields, especially the strains in the x and y directions. The
evaluation is conducted for
t=
40 s. An excellent agreement between the experiment and
the simulation is evident.
Figure 13. Comparison of the strain field of Abaqus and DIC in y-direction and x-direction.
5. Conclusions
This study investigated the material and damage behaviour of SLS PA12 under shear
loading and the application of Chaboche’s material model with the modified GTN model.
The main conclusions are the following:

Materials 2024,17, 38 13 of 15
1.
This study provides fundamental insights into the behaviour of SLS PA12 under shear
loading, which are relevant for a wide range of applications in materials science and
3D printing.
2.
The application of the Chaboche material model in combination with the modified
GTN model shows that complex material behaviours, such as those of SLS PA12 under
shear loading, can be successfully simulated, improving the prediction accuracy in
similar material studies.
3.
The results of this study extend the understanding of the damage behaviour of 3D-
printed materials and provide a valuable contribution to the further development of
reliable simulation models.
In summary, the precise determination of the shear factor
kw
enables an accurate
simulation of the material and damage behaviour of SLS PA12, which opens perspectives
for improved design and testing methods in additive manufacturing.
Author Contributions: Conceptualization, D.S. and M.Z.; Methodology, D.S.; Software, D.S., L.R.,
K.K., D.K. and P.M.; Validation, D.S.; Formal analysis, D.K.; Investigation, D.S., L.R., K.K., R.R. and
P.M.; Resources, L.R., K.K., D.K., R.R., P.M. and M.Z.; Data curation, P.M.; Writing—original draft,
D.S. and L.R.; Writing—review & editing, D.S., L.R. and M.Z.; Visualization, D.S., L.R. and R.R.;
Supervision, D.S.; Project administration, D.S. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The raw/processed data required to reproduce these findings can be
shared with interested researchers upon request.
Conflicts of Interest: The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported in this paper.
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