Tafm 2020 102497 PDF
Tafm 2020 102497 PDF
Tafm 2020 102497 PDF
A R T I C LE I N FO A B S T R A C T
Keywords: This paper presents experimental investigations on the geometrical and fracture properties of specimens ob-
Four-point bending tests tained by Additive Manufacturing technology. The experimental tests were performed on Single Edge Notch
Mode I and II fracture toughness Bend (SENB) specimens obtained through the Selective Laser Sintering process, based on the polyamide PA2200
Lased-sintered polyamide material. The SENB specimens were manufactured using three different process energies-PEs (E1, E2 and E3),
Process energy and spatial orientation
respectively three different spatial orientations-SOs (Vertical-V, Horizontal-H and Oblique-O). Symmetric and
asymmetric four-point bending tests were used to determine the mode I and II fracture toughness (KIC and KIIC).
It was observed that the density (ρ) of the 3D printed specimens is highly dependent on the PE and SO, the
highest density values being obtained for the highest PE (E1), respectively for the V-SO. Maximum relative errors
of the main geometrical parameters (thickness, length and width) of the SENB specimens were obtained for E3-
PE and H-SO. With respect to the fracture toughness, it was observed that, regardless of PE and SO, the KIC values
are higher than KIIC ones. The highest KIC value was found for E1 and V-SO, while KIIC highlight the highest value
for E1 and H-SO. Finally, analysis of variance (ANOVA) method is used to analyze the influence of various
factors on outcome parameters.
1. Introduction conduct numerical simulations using XFEM, and compare the results
afterwards. Brittle, ductile and kinked fracture behavior were asso-
One of the most outstanding features of additive manufacturing ciated with filament orientation during manufacturing process. Tensile
(AM) technology is the geometrical versatility of the parts that can be testing was extensively conducted on PA 12 (PA2200) [11–13]. The
produced, at relatively low manufacturing costs [1–3]. The properties effect on elongation to break and mechanical strength according to the
of the parts are close related to process parameters and due to the lack sinterization process was studied by Craft et al. [14]. Significant dif-
of standardization, the mechanical characterization is required for ferences were underlined according to the manufacturing process. The
every technology [4–6]. influence of loading configuration on the fracture toughness was de-
There are many efforts in characterization of AM parts. The strain termined by Poapongsakorn and Carlsson [15], on PVC foams using
rate influence of the additive manufactured PA12 on the failure load single edge-notched beam specimens in three and four-point bending.
was studied for tensile specimens [7]. The low rate tensile test was The results are showing significantly higher fracture toughness ob-
conducted in accordance with [8], while the high rate tests were con- tained in four-point bending test. Also, the linear relation between the
ducted using Hopkinson pressure bar, also in tension. Higher failure specimen density and KIC is revealed.
loads were recorded for higher strain rates. The stress-strain curves Crack growing in tensile test, according to building directions was
obtained for low tension rate exhibit non-linear behavior and provides studied by Riemer et al. [16], for titanium specimens produced by se-
similar mechanical properties to those of PA12 conventionally manu- lective laser melting. They proved that substantial improvement of
factured. Some other authors studied the influence of the surface aspect crack resistance behavior can only be achieved by heat treatment. Ex-
of AM parts as an important issue that directly derives from the process. tensive studies on full range loading conditions including pure dela-
The effect of surface roughness on the fatigue performances of titanium mination modes and mixed modes I/II, I/III and II/III were successfully
alloyed specimens was studied, underlining the crack initiation in re- conducted on different composite structures and porous materials
lation to surface integrity [9]. Specimens obtained by fused filament [17–20]. It was found that, in-plane and out-of-plane loading angle,
fabrication having different orientations were tested in order to de- density, testing conditions plays a decisive role on fracture toughness
termine the fracture behavior in layered materials [10]. Also, they [21–24]. The asymmetric four-point bending tests has received special
⁎
Corresponding author.
E-mail address: dan.stoia@upt.ro (D.I. Stoia).
https://doi.org/10.1016/j.tafmec.2020.102497
Received 23 December 2019; Received in revised form 16 January 2020; Accepted 16 January 2020
Available online 17 January 2020
0167-8442/ © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/BY-NC-ND/4.0/).
E. Linul, et al. Theoretical and Applied Fracture Mechanics 106 (2020) 102497
attention over the years [25–27]. Due to the relatively simple loading
configuration, different teams of researchers determined the fracture
behavior of concrete [28–31], granite [32–34], foams [35], pure tita-
nium [36] and extruded polystyrene [37] materials. Moreover, the
theoretical prediction of the experimental results was intensively stu-
died by Mirsayar and co-workers [38,39], Torabi and co-workers
[40,41], and Aliha and co-workers [42,43], using different theories and
fracture criteria. In addition, fracture properties determined using a
significant number of AM specimens were determined by Ahmed and
Susmel [44] on PLA and by Razavi and Berto [45] and Solberg et al.
[46] on metallic materials produced by laser melting.
To the best knowledge of the authors, there are no results reported Fig. 1. 3D specimen model.
in the literature related to mode I and mode II fracture toughness of
laser-sintered Polyamide, under four-point bending (4 PB) tests. 2.2.1. Specimen design and additive manufacturing
Therefore, for investigating the main fracture properties, this paper uses The specimen geometry (Fig. 1) was designed in SolidWorks 2017
single edge notch bend specimens in symmetric and asymmetric 4 PB according to the specifications of ASTM D 5045-99 standard [52]. The
testing fixtures. Also, the influence of three different process energies notch was designed on the 3D model of the specimen having a width of
and spatial orientations have been investigated. In addition, the influ- 0.3 mm and a total length of 10 mm and was formed during additive
ence of various factors on outcome parameters was analyzed using manufacturing process. In order to avoid the specimens wrapping and/
analysis of variance (ANOVA) method. or twisting during manufacturing process, the notch was closed on the
first 2.5 mm from the outer bottom surface. The bridge between the
crack flanks was removed mechanically using an electrical saw blade
2. Materials and methods
for cutting 2.5 mm in width of the specimen, along the notch direction.
The specimens were positioned in three ways that materialize three
2.1. Materials
spatial orientations (SOs): (i) vertical orientation (V = 90°) having the
width dimension (W) of the specimen along with the growing direction
This investigation is based on the polyamide PA2200 material used
(Z direction), (ii) horizontal orientation (H = 0°) having the thickness
for specimens manufacturing, which is an EOS (Electro Optical Systems
dimension (B) aligned with the Z growing direction, and (iii) oblique
- EOS GmbH, Germany) commercial product. In its powder form,
orientation (O = 45°) having the frontal plane of the specimen angular
PA2200 is suitable for sinterization, the resulted parts exhibiting good
oriented to the horizontal XY plane of the machine (see Fig. 2). Ten
physical and mechanical properties, despite the porous structure. The
specimens were organized for each SO and connection ribs were built in
internal structure of PA2200 is directly influenced by the following
order to prevent geometrical distortions.
main factors: process energy, layer thickness, particle size and powder
The additive process was conducted on EOS Fromiga P100 machine
spreading. Some physical, biological and mechanical properties were
determined by the producer: grain size of 56 µm according to ISO
13320-11 [47]; bulk density according to EN ISO 60 is 0.45 g/cm3 [48];
melting point 172–180 °C according to EN ISO 11357-1 [49]; bio-
compatibility according to EN ISO 10993-1 [50] and USP/level VI/
121 °C; food contact approval in compliance with the EU Plastics Di-
rective 2002/72/EC [51].
2.2. Methods
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E. Linul, et al. Theoretical and Applied Fracture Mechanics 106 (2020) 102497
using three different process energies (PEs): E1, E2 and E3, which are loaded SENB specimens (see Fig. 4a), while for KIIC an asymmetric
presented in the Table 1. The parameters from Table 1 presents the loading configuration was assumed (see Fig. 4b).
follows notations: P-laser power; v-scanning velocity; E-energy density, Dimensions and loading configuration of 4 PB test specimens are
as function of power, velocity and scan spacing; d-scan spacing; h-beam also shown schematically in Fig. 4. The distance between the supports
offset; T1-temperature of the building chamber; T2-temperature of the for the symmetrical fixture was set at 4W (≅80 mm), while the loading
removal chamber; t-layer thickness; SF-scaling factors on XY and Z di- points at a distance of 2W (≅40 mm). In the case of asymmetrically
rections. Powder bed is the height of the non-sintered powder placed at loaded SENB specimens, the distance between the supports and the
the beginning and at the end of the manufacturing process. loading points (b1 + b2) was considered as equal to five times the
By positioning 10 specimens for each spatial orientation and con- width/thickness of the specimen (5B), that is about 50 mm
sidering 3 process energies, a total number of 90 specimens were (b1 = 10 mm and b2 = 40 mm). In both cases (symmetric and asym-
manufactured. metric loading), as mentioned above, the specimen crack (a) kept the
Formiga P100 machine uses a 30 W CO2 laser for layer-by-layer same length (a ≅ 10 mm), and the load was applied along it (parallel to
sinterization of plastic powders. It consists of two main chambers: the crack flank) [35]. Aliha and co-workers [54,55] showed that for
building chamber, were the process occurs and the removal chamber small values of b1/W ratio, the effect of T-stress on mode II deformation
were the parts are lowered and cooled down. The chambers are set up is high. Therefore, in choosing the dimensions of the specimens, it was
to different temperatures: 170 °C for building and 159 °C for removal taken into account that the location of supports and their distance from
through independent electrical heating sources. The heat convection the crack tip do not significantly affect the crack tip stress field.
and conduction ensure the softening temperature for the powder in the The experimental tests under 4PB fixture were performed in ac-
building chamber, so that the laser gives only the additional energy cordance with ASTM D 5045-99 standard [52], while the testing tem-
required for sinterization. The oxygen content of the chambers in perature was controlled to be within the range 25 ± 2 °C.
controlled by the machine under 0.5%.
The powder is flowing from two barrels placed on the top of the 2.2.4. Data processing and statistics
machine, and it is uniformly spread by a mechanical arm using a In order to validate the data and to determine the significance of the
sweeping blade. recorded differences, one-way analysis of variance (ANOVA) was used
The laser beam has the focal plane on the zero level of the building for the outcome parameters: density, length, thickness, width, mode I
chamber and a spot diameter of 0.42 mm. The spot size is therefore fracture toughness and mode II fracture toughness, in relation to the PO
directly limiting the minimum wall thickness of a part. (E1, E2 and E3) and SO (V, H and O). In addition, the Pearson’s cor-
The additive process runs for 9 h for each energy. At the end of relation was used to determine how strong is the relation between input
manufacturing, the parts cool down for another 18–20 h and after that technological variables and outcome parameters [56].
were removed from the machine (Fig. 3) and air blasted.
3. Results and discussions
2.2.2. Mass and geometry assessment
Next step in study was to determine the mass and linear dimensions 3.1. Geometric properties
of each individual specimen, in order to compute the density (ρ) and to
verify the relative dimensional error. The measurements were con- For all 90 specimens, linear measurements were conducted prior to
ducted on L, B and W dimensions using a Mitutoyo digital caliper of mechanical testing. For each specimen different geometrical parameters
0.02 mm accuracy. All measurements were repeated three times in (L, B and W) were acquired three times and the average value of these
order to obtain average value of every dimensional parameter/spe- was further taken into consideration. The measured values (mval) were
cimen. then used together with the nominal dimensions (nval: L = 92.1 mm,
The specimens were then weighted using a Kern laboratory balance B = 10.23 mm and W = 20.46 mm) in order to determine the relative
of 0.01 g accuracy. Having the mass and computing the volume for each error, in accordance to the Eq. (1).
specimen, the individual densities were obtained.
By visual inspection, it was observed that the obtained laser-sin- mval − nval
Err[%] = ·100
tered specimens had no defects, such as pores, separation of layers or nval (1)
cracks, and no signs of internal stress were detected. The density of the specimens is highly dependent on the SO and PE
(Fig. 5). The values here presented are averages and as we expect higher
2.2.3. Fracture properties assessment energy of sinterization (E1) conduct to higher density due to larger
All experimental tests were carried out using a Zwick Roell standard fusion bridges between powder particles. From the orientation point of
electromechanical universal testing machine with a maximum load-cell view, V-SO of the specimen always lead to better density. This may be
capacity of 5 kN, controlled by a constant crosshead displacement of the influence of the powder spreading in relation to the specimen or-
5 mm/min for all specimens. For the evaluation of the fracture prop- ientation (sweeping blade generates a local settle down of the powder.),
erties, four-point bending (4 PB) tests and single edge notch bending and the number of layers that composes the part (200 layers). The
(SENB) specimens were adopted [53]. The loading configuration of the standard deviation of density shows a slight data spread.
investigated specimens was designed to obtain both the mode I (KIC) Maximum relative errors (%) of geometrical parameters were re-
and mode II (KIIC) fracture toughness values. corded for specimen thickness in the case of E3-PE and H-SO (about
Details of experimental testing set-up and used procedure are pre- 9.5%). As can be seen in Fig. 6a, less dependent dimensional error in
sented in Fig. 4. Assessment of KIC was performed on symmetrically relation to the PE and SO was obtained for the total length of the
Table 1
Laser sintering parameters.
SO [ °] P [W] v [mm/s] E [J/mm2] No. of layers d [mm] h [mm] T1 [°C] T2 [°C] t [mm] SF [%] Powder bed [mm]
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Fig. 3. Images of the specimens before machine removing: V (a), H (b) and O (c) spatial orientations.
specimen (L), meaning that larger dimensions are less influenced by the
process parameters [11–13]. The thickness error (Err B) was very si-
milar for the E1 and E2 energies, with low standard deviation and
identic trend regarding the SO (see Fig. 6b). The errors determined for
E3-PE however are proving a dimensional instability of the SLS process.
The error of specimen’s width (Err W) seems to be very low and
consistent for all three PEs in the case of V-SO of the specimens (see
Fig. 6c). On the other hand, the horizontal positioning (H-SO) lead to
high relative errors very dependent on PE.
As a general observation, the growing direction of the specimens (Z
direction of machine) determine smaller relative errors, as it can be
observed from Fig. 6b and c (orientation O-SO for Err B and V-SO for Err
W). Another conclusion that emerged from the error graphs is that
higher PE influences the dimensional stability of the process in a con-
venient manner.
Fig. 4. Experimental set-up for symmetric (a) and asymmetric (b) loading configuration.
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E. Linul, et al. Theoretical and Applied Fracture Mechanics 106 (2020) 102497
Fig. 6. Relative error of length (a), thickness (b) and width (c) according to PE and SO.
ultimate load capacity (maximum load) is found. Once the peak load 3PQ l
σ=
was reached, the specimen either breaks suddenly (e.g. Fig. 8b curve for BW 2 (4)
the V-SO) or shows a progressive decrease in load carrying capacity
(e.g. Fig. 8b curve for the O-SO), followed by a brittle fracture [61,62]. PQ − Q
τ0 =
Notably, the progressive decrease in load have been found for speci- BW (5)
mens printed in the O-SO direction, while a sudden brittle fracture was
obtained for the other two SOs (H-SO and V-SO). were l (distance between the first support and the first loading
As can be observed from Figs. 8 and 9, the P-Δ curves obtained from point) = W (specimen height) in [mm], B is specimen thickness (depth)
specimens in the same group presents major differences, which means in [mm] and PQ is the critical fracture load in [N]. Taking into account
that both the PE and the SO significantly influence the fracture behavior the suggestions of the ASTM D5045-99 standard [52], the determina-
of the investigated SENB specimens. From Fig. 8 it can be observed that tion of the critical fracture load PQ from the P-Δ curves was done ac-
the SO presents the highest differences in terms of load and displace- cordingly.
ment, this being observed especially for symmetrical loading (mode I From Fig. 4b it can be seen that the asymmetric configuration is
fracture). On the other hand, PE has major differences in terms of both both in static equilibrium and statically determined. Therefore, in Eq.
loading configuration (symmetric, asymmetric) and SO. (5) the shear force, Q, which acts between inner loading points, is re-
The analysis of the P-Δ curves represents an important aspect be- lated to the force PQ and is given by Eq. (6) [64]:
cause depending on their interpretation the fracture toughness will be
(b2 − b1 )
calculated. The mode I (KIC) and mode II (KIIC) fracture toughness were Q = PQ
(b2 + b1 ) (6)
determined according to [63] based on Eqs. (2) and (3):
Finally, the geometric stress intensity factors fI(a/W) and fII(a/W),
a
KIC = σ πa ·fI ⎛ ⎞ expressed in terms of ratio between crack length and the height of the
⎝w⎠ (2)
specimen a/W, are determined for both loading fixtures (symmetric and
asymmetric configurations) using the polynomial Eqs. (7) and (8), as
a follow [63]:
KIIC = τ0 πa ·fII ⎛ ⎞
⎝w⎠ (3)
a a a 2 a 3 a 4
fI ⎛ ⎞ = 1.122 − 1.121 + 3.740⎛ ⎞ + 3.873⎛ ⎞ − 19.050⎛ ⎞
where a is the crack length in [mm], while σ and τ0 [MPa] are the ⎝W ⎠ W ⎝W ⎠ ⎝W ⎠ ⎝W ⎠
normal and shear stresses corresponding to the mode I and II loading, a 5
+ 22.550⎛ ⎞
and are calculated with the Eqs. (4) and (5) [63]: ⎝W ⎠ (7)
Fig. 7. Initial (a, e) and tested (c, g) 4PB specimens under mode I and II loading.
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E. Linul, et al. Theoretical and Applied Fracture Mechanics 106 (2020) 102497
Fig. 8. Load-displacement curves under mode I (a, b, c) and mode II (d, e, f) fracture. Influence of SO.
a a a 2 a 3 and O-SO (for E1 and E2), while in the V-SO, lower values are obtained
fII ⎛ ⎞ = −0.2915 + 6.3229 − 9.1199⎛ ⎞ + 6.0570⎛ ⎞
⎝W ⎠ W ⎝W ⎠ ⎝W ⎠ (8) with about 15% (Fig. 10b). It was found that the KIIC values for E3 do
not follow the same pattern with the other two energies (E1 and E2).
It should be mentioned that for asymmetric four point pending a This aspect may be associated with the difficult placement of the spe-
small amount of Mode I stress intensity factor is present due to the finite cimens due to geometrical errors (see Section 3.1). The mode I of
geometry of the specimen [63]. However, this value is approximately fracture did not meet these problems because the loading was done
18 times smaller than the Mode II value and was neglected in the fur- symmetrically.
ther calculations. Analyzing Fig. 11 it can be observed very easily that regardless of
In order to highlight the dependence of the KIC and KIIC values with the SO, all the KIC and KIIC values decrease significantly with the de-
the specimen density (ρ), it is necessary to introduce a new parameter, crease of PE. However, taking into account the SO, the largest differ-
called fracture toughness index IK. Parameter IK is defined for each ences in KIC and KIIC values, up to about 79%, are obtained for the H-SO
loading mode (mode I and II) by the Eq. (9) [65]: (from E1 to E3). In contrast, the V-SO shows the smallest decreases in
KiC KIIC values (up to 40.18%) depending on the PE decrease (see Fig. 11b).
IK , i = , i = I ,¯II [MPa·m3.5/kg] On the other hand, from Tables 2 and 3 (last column) it can be
ρ (9)
deduced that KIC and KIIC are density-dependent, the density of speci-
Taking into account all the Eqs. (2)–(9), Tables 2 and 3 lists the mens highlighting a major influence on the fracture toughness values.
average values of the obtained results for both symmetric and asym- Considering this density-properties dependence, Fig. 12 shows the
metric loading configurations. The experimental results are presented variation of fracture toughness (KIC and KIIC) data with the specimen’s
for both SO and PE. density (ρ).
Figs. 10 and 11 show the variation of the fracture toughness (KIC It has been observed that regardless of the loading configuration
and KIIC) with PE, respectively SO. From these figures, it can be ob- (symmetric or asymmetric), PE (E1, E2 or E3) and SO (H, V or O), the
served that both PE and SO have significant influences on KIC and KIIC. mode I and mode II fracture toughness values increase with increasing
Regardless of PE and SO, the KIC values are higher than the KIIC values; of specimen’s density. In most cases, with very small exceptions, this
this being consistent with the literature reported results on other types increase is linear.
of polymeric materials [20,25,66]. From Fig. 10a it is observed that KIC Fig. 12 actually displays some maps of distribution of KIC and KIIC
respects the same pattern according to the used PE. The highest KIC values according to PE and SO. These maps have a particular im-
values are obtained for V-SO, followed by O-SO and H-SO respectively. portance in the optimization processes of the materials used in different
The mode I fracture toughness values in the V-SO is higher by up to engineering applications. Therefore, knowing the type of used material
51.86% (for E1) compared to the one in the H-SO. This difference in- (in this case PA 2200), by visualizing these fracture toughness-density
creases linearly up to 69.81% (for E3) with the decrease of PE. Mode II maps, one can predict the values of KIC and KIIC without carrying out
fracture toughness presents approximately the same values for H-SO 4PB experimental tests. This helps to eliminate the time of production
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Fig. 9. Load-displacement curves under mode I (a, b, c) and mode II (d, e, f) fracture. Influence of PE.
of the specimens and to carry out the experimental tests, respectively to case, both loading modes I and II lead to lower fracture strength of the
reduce the costs regarding the production and the testing of the spe- layer interface than the layer itself. Therefore, the crack direction has a
cimens. Ultimately, it is desirable to make such distribution maps of the preference growth (shear effect) along the layer bonding interface. This
properties for different engineering materials tested under different debonding is followed by the crack growth, which for mode I tends to
loading conditions. propagate in the plane of the crack (Fig. 13c), while for mode II the
Typical mode I and II fracture paths of broken laser-sintered spe- path ends under the loading point (Fig. 13f). The samples growth in the
cimens obtained using E1 process energy are shown in Fig. 13. Based on horizontal and oblique position have a notch direction parallel and
the experiments, PE does not affect the crack propagation paths, while respectively oblique to the layer deposition and bonding, and therefore
SO substantially changes the fracture path. The mode I fracture path in no debonding effect is recorded.
H and O directions is stable and grows following a straight line along Based on Fig. 13, all the SENB specimens made of Laser-Sintered
the notch plane (Fig. 13a, b). For mode II loading, the crack initiation Polyamide were fractured from the crack tip without any local damage
makes an angle to the notch plane, of following values: 54.5° for H- from supports or loading points.
direction of sample grow and 58.4° for the V-direction (Fig. 13d, e).
Finally, the propagated crack stops under the nearest loading point,
completing the test. 3.3. Data statistics
The samples having vertical direction of growing possesses a notch
direction perpendicular to the layer deposition and bonding. In this Quasi-static Pearson’s correlations (see Table 4) evidence a linear
relation between the additive parameters: process energy PE and spatial
Table 2
Mean values of mode I fracture properties according to PE and SO.
Process energy Spatial orientation ρ [g/cm3] Fmax [N] PQ [N] Q [N] σ [MPa] KIC [MPa·m0.5] IK,I [MPa·m3.5/kg]
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E. Linul, et al. Theoretical and Applied Fracture Mechanics 106 (2020) 102497
Table 3
Mean values of mode II fracture properties according to PE and SO.
Process energy Spatial orientation ρ [g/cm3] Fmax [N] PQ [N] Q [N] τ0 [MPa] KIIC [MPa·m0.5] IK,II [MPa·m3.5/kg]
Fig. 10. Mode I (a) and mode II (b) fracture toughness variation according to PE. Influence of SO.
Fig. 11. Mode I (a) and mode II (b) fracture toughness variation according to SO. Influence of PE.
orientation SO and the outcome variables: density ρ, length L, thickness each spatial orientation (p ≪0.05). The highest significant difference of
B, width W, mode I fracture toughness KIC and mode II fracture energy-density relation is recorded for vertical spatial orientation (V-
toughness KIIC. Strong positive correlation of density with both additive SO) of the specimens (p = 1.3 · 10−22 and F = 785.31). In addition, a
parameters (PE and SO) can be observed. The length L of the specimens trend of difference increasing among densities can be observed as the
shows very little connection with the SO for E1, while the thickness B specimens modified their spatial orientation from H-SO to V-SO.
shows a strong negative correlation with the SO, for all three PEs (E1, The fracture toughness determined for modes I and II fracture were
E2 and E3). The KIC confirm a strong positive correlation with both PE verified for statistically significance according to the PE and the SO (see
and SO, while KIIC has positive correlation only for the PE and negative Table 6). Without exception, significant differences among KIC results
correlation for SO. and KIIC results were determined (p ≪ 0.05).
In order to demonstrate the statistical signification of the outcome Therefore, the PE used for sinterization on one hand and the SO of
variables, the one-way ANOVA was used for density and fracture the specimen in the building envelope on the other hand are directly
toughness determined for all SOs (H, V, O) and all PEs (E1, E2, E3). The and strongly influencing the fracture toughness. As orientation modifies
ANOVA parameters presented are: Source of Variation – Between from H-SO to V-SO, larger influence of the PE is recorded (exponential
groups (BG) and Within Groups (WG); Sum of squares (SS); Degrees of decrease of p value) for specimens subjected to mode I fracture. On the
freedom (df); F value (F); P value (p) and F critic (F crit.) [67]. other hand, a reversed phenomenon was determined for mode II frac-
According to Table 5, statistically significant differences between ture.
the specimens densities obtained at E1, E2 and E3 were determined for
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E. Linul, et al. Theoretical and Applied Fracture Mechanics 106 (2020) 102497
Fig. 12. Mode I (a) and mode II (b) fracture toughness variation with specimen
Declaration of Competing Interest
density.
Fig. 13. Mode I (a-c) and mode II (d-f) crack propagation paths of Laser-Sintered Polyamide.
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E. Linul, et al. Theoretical and Applied Fracture Mechanics 106 (2020) 102497
Table 4
Pearson’s correlation of outcome parameters with energy and orientation.
Parameter SO (E1) Orient. (E2) SO (E3) PE (V) PE (H) PE (O)
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E. Linul, et al. Theoretical and Applied Fracture Mechanics 106 (2020) 102497
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