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A combined theoretical and experimental approach to model polyamide 12

degradation in selective laser sintering additive manufacturing

Feifei Yang1, Xu Chen1

*

1Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA

Abstract: Selective laser sintering (SLS) generates complex high-performance parts from micrometer-

diameter powders. In polyamide 12 SLS, a considerable amount of expensive polyamide 12 materials

remains un-joined in the additive manufacturing (AM) process. Such materials, particularly the ones near

the heat-affected zones (HAZ), go through irreversible chemical degradations originated from thermal

oxidations. Despite efforts in understanding the degradation mechanisms of the materials, full modelling of

the complex material degradation remains not well understood. In this work, through a combined theoretical

and experimental approach, we propose a first-instance kinetic model considering the effects of both oxygen

and laser to model the material degradation in polyamide 12 SLS. By mapping the actual material

degradation rates into the oxidation physics and data-driven parameter identification, we obtain the

coefficients of the actual coupled oxygen and laser effects. Through sensitivity analysis, we derive the

fitting equations between the sample degradation rates and the oxidation time. The proposed kinetic model

can predict the oxidation rates of pure or mixed materials using two easily available parameters: materials

density and oxidation time. We show that the laser effects are 4-time stronger than oxygen effects on

polyamide 12 degradation. The predicted oxidation matches on average 89.53% with the actual SLS

degradation rates, in contrast to a 34.48% accuracy from a basic autoxidation model. Besides, the paper

identifies how coupling of oxygen, laser irradiation, and preheating impacts the rate of material degradation.

Key words: Kinetic modelling; Polyamide 12; Thermal oxidation; Coupled oxygen and laser effects;

Selective laser sintering

1. Introduction

Additive manufacturing (AM) is a collective term with unrivalled design freedom to fabricate

functional applications by joining layers of materials on top of each other [1-3]. Selective laser sintering

(SLS) is a popular powder-based AM process with superior potentials to produce products with high

mechanical properties and good thermal stability compared to other 3D additive techniques [4,5]. The

capability to process almost any material, including polymers, metals, ceramics, and many types of

composites, further extends the popularity of SLS [6]. Supporting materials are not needed in SLS as the

powders can directly act as support to the printed parts [7]. Resulting from the high flowability, high melting

*

Corresponding author.

Email addresses: yangff@uw.edu (Feifei Yang), chx@uw.edu (Xu Chen).

enthalpy, and sharp melting peak, polyamide 12 appears to be the most suitable material among the wide-

ranging material scope appliable for SLS [8-10]. Polyamide 12 (and its compounds) takes up approximately

90% of complete industrial consumption [11].

The extensive usage of polyamide 12 powders in SLS results in a large amount of un-sintered powders

after going through complex degradations [12-14]. Previous research revealed that irreversible oxidation

and post-condensation dominate the aging process and change the polymer chemical structures by chain

scission, branching, and chain cross-linking [13,15,16]. The macro-structural chain cross-linking attributes

to an increase in the material molecular weight and a decrease in the melt flow index (MFI) [17,18]. As the

molecular weight increases with the powder aging, melt viscosity also increases and powder flowability

decreases [14,16]. Aging affects little the distribution of powder sizes but leads to the deteriorated thermal

property and reduced surface morphology [13].

Despite the property changes, a considerable amount of un-sintered polyamide 12 residues (80% -

90%) has the potential to be reused for further applications [14]. One of the solutions to the successful reuse

of SLS residue is to fabricate the powder residue into feedstock for other AM processes without

significantly reducing its value. Polyamide 12 powder for SLS is priced at around $150/kg (in 2020

currency). The cost of extrusion-based additive manufacturing (EAM) or fused deposition modelling (FDM)

polyamide 12 filament is approximate $100/kg, while the cost of polyamide 12 pellets for conventional

plastics processing is below $3/kg [19]. It is more economical to process the polyamide 12 powder residue

into filaments for EAM or FDM rather than pellets for conventional plastics processing [19,20]. The

common practice of reusing the polyamide 12 powder residue in SLS is to mix 50% new powders with 50%

reclaimed powders from past experiments [13,19].

Besides, several research works dedicated to better understand the aging mechanisms of polyamide 12

in SLS. Diller TT et al. [21] built computational models at two complexity levels, a one-dimensional model

and a two-dimensional finite element model, to explore the influences of heat transfer on the aging of

polyamide 12 in SLS. Yuan M et al. [22] measured thermal conductivity of fresh and aged polyamide 12

powders to establish a baseline for thermal aging control in SLS. Dadbakhsh S et al. [13] examined new

and aged polyamide 12 powders along with their mixtures to identify the effect and mechanisms of in-

process aging on material thermal and coalescence behaviors in SLS. Chen P et al. [12] investigated the

aging mechanisms and microstructural evolution of polyamide 12 in SLS. Bernard et al. [23] performed

thermogravimetric experiments with mass spectrometric analysis to obtain the kinetic parameters on the

thermal degradation of polyamide 12 in SLS.

Heated and exposed to intensive laser radiations, the nature of material degradation in SLS involves

coupled thermal and laser-induced oxidation reactions. Despite the previous works, the kinetics and the full

modelling of polyamide 12 degradation in the complex SLS remain not well addressed. We propose a first-

instance kinetic scheme considering both the oxygen and laser effects to model material degradation in SLS

through multi-physics modeling and data-driven parametric identification. In this work, we conduct SLS

printing experiments and calculate the actual polyamide 12 degradation rates through Fourier-transform

infrared spectroscopy (FTIR) results and Beer-Lambert’s law. By data-driven parameter identification of

the actual SLS degradation rates into the oxidation model, we obtained the coefficients of actual coupled

oxygen and laser effects in SLS. Through a further sensitivity analysis, we derive the relationship between

the sample degradation rates and oxidation time. The proposed model can predict the degradation rates of

materials using materials density and oxidation time. The new kinetic model applies to not only pure

material but also mixed powders. Furthermore, using the proposed kinetic model, we identified the

influences of the coupled oxygen, laser irradiation, and preheating on the rates of material degradation in

the SLS of polyamide 12. The findings provide new knowledge of quantitative influences of the process

parameters on material degradation and on approaches to reduce oxidation in SLS.

2. Method

Figure 1 presents an overview of the proposed research approach. We discuss the details of each step

in the following sections.

Degradation rates

SLS experiment

Basic autoxidation scheme of polymer

Oxidation mechanism of polyamide 12

Conventional oxidation model of polyamide 12

FTIR

Theoretical Experimental

Comparisons between the model results and experimental results

Oxygen effectsCoupled laser and oxygen effects

Basic autoxidation

model

SLS sample group 1

Coefficients of aging SLS sample group 2

Data-driven parameter

identification

Sample density

Aging time

The proposed model

Model verification

Basic autoxidation

model

Figure 1 The proposed approach to build the kinetic scheme of polyamide 12 aging in SLS considering the coupled

oxygen and laser effects

2.1. Oxidation model

2.1.1. Mechanism of thermal oxidation

Constituted of polymethylenic sequences and the amide group (-NHCO-), polyamide 12 has the

following chemical structure:

–[–CH2–

O

‖

C–N

H

–(CH2)10 –CH2–

O

‖

C–N

H

–(CH2)10 –CH2–

O

‖

C–N

H

–]–n

From the basic autoxidation scheme of polymers [24,25], high temperatures initiate the thermal

oxidation of polyamide 12 materials to form alkyl radicals P• (Eq. 1). Incorporation of oxygen and

abstraction of hydrogen atoms propagate oxidation of polyamide 12 [15]. In the propagation stage (Eqs. 2-

3), alkyl radicals P• combine with O2 to form peroxy radicals PO2•. PO2• captures hydrogen atoms from

polymer substrates to further produce hydroperoxides. Thermal decomposition of the hydroperoxide groups

is the main mechanism of polymer oxidation below 200 °C. Such a process involves a unimolecular mode

(Eq. 4) and a bimolecular mode (Eq. 5) [26,27]. Hydroxyl radicals PO•, alkoxy radicals HO•, and peroxy

radicals PO2• with polymer substrate rapidly interact and form two balance reactions (Eqs. 6-7) [15]. This

process also involves chain scission (S) and hydrogen abstraction.

PH Polyamide 12k1

P• (1)

P• + O2

k2

PO2• (2)

PO2• + PH k3

POOH + P• (3)

POOH k4

PO• + HO• (4)

2POOH k5

PO• + PO2• + H2O (5)

Balance reactions:

POOH k6

2P• + PNH2• + PH=O + H2O + S [-2PH, -CN] (6)

2POOH k7

P• + PO2• + PNH2 + PH=O + H2O + S [-PH, -CN] (7)

Here, parameters ki’s are a series of elementary reaction constants of the thermal oxidation.

The termination reactions of alkyl radicals P• involve coupling or disproportionation (Eqs. 8-9), where

F and X denote double bonds and chain crosslinking (X), respectively. The termination reactions of peroxy

radical pairs are ascribed as Eqs. 10-13. Peroxy radical pairs first react to form the transition cage [PO••

OP]cage with oxygen. The transition cage further generates final products (e.g., POOP, NH(P=O)2, and PNH2)

together with chain crosslinking (X) and scission (S).

P• + P• k8

γ1PP + 1-γ1PH + 1-γ1F + γ1X -1-γ1PH (8)

P• + PO2•k9

γ2POOP + 1-γ2POOH + 1-γ2F + γ2X -1-γ2PH (9)

PO2• + PO2•k10

PO••OPcage + O2 (10)

[PO••OP ]cage

k11

POOP + X (11)

[PO••OP ]cage

k12

NH(P=O)2 + PNH2 + PH=O + S [-CN] (12)

[PO••OP ]cage

k13

2P• + 2PNH2 + 2PH=O + 2S [-2PH, -2CN] (13)

2.1.2. Basic autoxidation model

The fundamental kinetics led to a basic model on thermal oxidation of polyamide 12 materials, defined

as the basic autoxidation model. The solution involves 5 main non-linear differential equations (Eqs. 14-

18) [15] indicating the derivatives of the compound concentrations with respect to time. For instance, the

rate of concentration changes of [POOH] (Eq. 14) equals the formation rates (POOH formed in Eqs. 3 and

9) minus the consumption rates (POOH consumed in Eqs. 6 and 7). We define the coefficient of oxygen

effect as (Eqs. 15, 16, 19), relating close to the oxygen concentrations O2. equals 1 in the basic

autoxidation model.

d[POOH]

dt = -k6fPHPOOH - 2k7fPHPOOH2 + k3PHPO2• + 1-γ2k9fPHP•PO2• (14)

d[P•]

dt = 2k6fPHPOOH + k7fPH[POOH]2- k2O2P•+ k3PHPO2•- 2k8P•2-

k9fPHP•PO2• + 2k13fPHPO••OPcage (15)

d[PO2•]

dt = k7fPH[POOH]2 + k2O2P•- k3PHPO2•-

k9fPHP•PO2•- 2k10PO2•2 (16)

d[PO••OP]cage

dt =k10[PO2•]2- k11 + k12 + k13fPH PO••OPcage (17)

d[PH]

dt = -2k6fPHPOOH- k7fPHPOOH2- k3PHPO2•- 1-γ2k9fPHP•PO2•

- 2k13fPH PO••OPcage (18)

Here, fPH is defined to avoid negative concentrations of substrate. fPH=[PH]/([PH]+ε) and ε=0.01 [15]; the

parameter itself does not significantly influence the oxidative kinetics.

From the mechanistic scheme in section 2.1.1, we also obtain the concentration changes of the

following reactants and products [15]:

d[O2]Consumed

dt = k2O2P•- k10PO2•2 (19)

d[PNH2]

dt = k6fPHPOOH + k7fPH[POOH]2 + k12+2k13fPHPO••OPcage (20)

d[PH=O]

dt =dPNH2

dt (21)

d[NH(P=O)2]

dt = k12[PO••OP]cage (22)

d[C-N]

dt = -dPNH2

dt (23)

dS

dt =dPNH2

dt (24)

dX

dt = γ1k8[P•]2 + γ2k9fPHP•PO2• + k11PO••OPcage (25)

Chain scission (S) occurs simultaneously with the oxidation-related signal diminishment near the

wavelengths of 1369.23, 1159.03, 1062.60, and 948.82 cm-1 [12]. In the basic autoxidation model, we define

the degree of chain scission (S) (Eq. 24) occurring in unit time (s) as the modelling aging rate for

polyamide 12 sample i.

S

(26)

where S is the degree of chain scission in oxidation time . We use Matlab ODE23s to solve the model

when knowing the initial concentrations of the main component and the elementary reaction coefficients ki.

We will introduce the details of these parameters in section 2.2.3.

At a specific temperature (e.g., a pre-heating temperature of the SLS machine, 160 °C), the elementary

reaction coefficients ki remain unchanged. However, the oxygen effect O2 can vary significantly at a

specific temperature when at different atmosphere, and largely affects the rates of material degradation.

Stronger oxygen effects result in faster degradation rates. In SLS, the nature of material degradation

involves the coupled oxygen and laser effects. The laser has even stronger effects than oxygen effects on

material degradation. Thus, the coupled laser and oxygen effects are substantially more significant than the

single oxygen effects on material degradation. However, it is difficult or impossible to get laser effects

using the modelling-only approach. Through experimentation, we shall get the actual material degradation

rates to derive the coefficients of the coupled laser and oxygen effects, referred to as

, through mapping

experimental results to the modelling results.

shows the enhancement effects on material degradation

from oxygen to the coupled laser and oxygen.

O2 is the coupled laser and oxygen effects in SLS.

2.2. Experimentation

2.2.1. SLS printing using polyamide 12 powders

We sintered different polyamide 12 combinations. The SLS machine used is an in-house built open-

configuration SLS AM research testbed with a 100 W Coherent GEM100A CO2 laser and a Scanlab

intelliSCAN 14 scanner (Figure 2). The parameter settings used in the printing experiments are: 160 °C

preheating, 3000 mm/s scanning speed, 18 W laser power, 0.3 mm scan spacing, and 150 µm layer thickness.

Table 1 exhibits the 22 kinds of printed samples with calculated density and oxidation time (time in the

chamber), i=1, 2, …22. In detail, the oxidation time is the sum of the preheating, printing and the post-

heating time. For part samples in this work, the preheating time is 5 minutes, and the printing time is 2

minutes. We change the post-heating time (20 seconds, 60 seconds, 120 seconds and 300 seconds) to obtain

part samples with different oxidation time.

Table 1 SLS printed samples using polyamide 12 powders, the calculated density, and oxidation time

Samples

Density/g·cm-3

Oxidation time/seconds

Parts using 100% new powders

0.9

440; 480; 540; 720

Parts using 70% new and 30% aged powders

0.828

420; 720

Parts using 60% new and 40% aged powders

0.804

420; 720

Parts using 50% new and 50% aged powders

0.78

420; 720

Parts using 40% new and 60% aged powders

0.756

420, 720

Parts using 30% new and 70% aged powders

0.732

420; 720

Parts using 20% new and 80% aged powders

0.708

420; 720

Parts using 10% new and 90% aged powders

0.684

420; 720

Parts using 100% aged powders

0.66

440; 480; 540; 720

* Polyamide 12 new powders are purchased from EOS Corp. Polyamide 12 aged powders are reclaimed from standard SLS

processes on an EOS P 390 machine.

Figure 2 SLS testbed and samples

2.2.2. Measured material degradation rates

In the polyamide 12 FTIR spectra, the dramatically diminished signals of peaks near wavelengths of

1369.23, 1159.03, 1062.60, and 948.82 cm-1 indicate the oxidation of amide groups [12]. We conducted

FTIR tests on the specimens in Table 1 as well as the pure polyamide 12 powder to examine the aging-

related signals using a Nicolet Magna-IR 560 FTIR instrument (wavelength ranges: 6500 cm-1-100 cm-1,

spectral resolution: 0.35 cm-1). The FTIR of powder (new powder) serves as the benchmark against the

degradation comparison. For specimen i, through the FTIR results and Beer-Lambert’s law (Eq. 27) [15],

we calculated the concentrations of the four oxidation-related components Yn (n=1, 2, 3,4) (corresponding

to peaks near 1369.23, 1159.03, 1062.60, and 948.82 cm-1), respectively.

Abs

(n=1,2,3,4)(27)

where Abs

,

and

are, respectively, the absorbance, the coefficient of molar absorptivity, and the

concentrations of the chemical component Yn; and is the thickness of the tested sample i. We obtain the

absorbances from FTIR results, and get the coefficients of molar absorptivity from the new powder

(benchmark sample). For the new powder, we read the tested thickness and absorbances from FTIR, and

calculate the molar concentrations using density and molar mass [28]. Then we get the coefficients of molar

absorptivity using the Beer-Lambert’s law [15], and insert these coefficients in Eq. 27 to calculate

concentrations of chemical component for part samples. We write

as the difference of

between the

benchmarked powder materials and the 3D-printed samples. As there are four peaks for each specimen i,

we write (in mol/L) to denote the average of

,

,

, and

for specimen i. We define the

actual degradation rate (involving both oxygen and laser effects) as the average concentration changes

of the oxidation-related components in unit time (Eq. 28), in mol/(L·s):

(28)

where i is the sample index in Table 1, and is the associated oxidation time.

2.2.3. Comparisons between the actual SLS degradation and the modelling aging rates

Specimen density and oxidation time in Table 1 are important parameters for the basic autoxidation

model. Besides, the initial concentrations of reactants are necessary to run the model. For each specimen i,

we get the initial concentrations of reactants, namely, POOH, PH and C-Nin the basic autoxidation model

(Eqs. 14-25) using the molar concentration formula

c

reactant-R=qi

M (29)

where c

reactant-R (in molar/L) is the initial molar concentration of reactant R (POOH , PH or C-N) in

specimen i; q

(in g/cm3) is the density of specimen i; M (in g/mol) is the molar mass of polyamide 12. In

the basic autoxidation, the initial concentrations of P•, PO2•, [PO••OP]cage, [O2]Consumed, PNH2, PH=O,

NH(P=O)2, S, and X are zero because they are intermediate products. The oxygen concentration, [O2], is

3.6×10-4 mol·L-1 [15] in the air atmosphere. Table 2 lists the elementary reaction coefficients for thermal

oxidation of polyamide 12 at 160 °C [26,27,29]. Inserting the above parameters in the basic autoxidation

model, we get the modelling aging rate for sample i, and compare the result to the actual degradation

rate .

Table 2 The elementary reaction constants for thermal oxidation of polyamide 12 at 160 °C [26,27,29]

Parameter

Value

Parameter

Value

k2 (L·mol-1·s-1)

108

k10 (L·mol-1·s-1)

1.6×1011

k3 (L·mol-1·s-1)

45.8

k11 (s-1)

2.0×108

k6 (s-1)

8.0×10-4

k12 (s-1)

3.4×108

k7 (L·mol-1·s-1)

6.0×10-3

k13 (s-1)

2.2×109

k8 (L·mol-1·s-1)

8.0×1011

γ1 (%)

50

k9 (L·mol-1·s-1)

5.0×1011

γ2 (%)

50

2.3. Kinetic model of polyamide 12 aging in SLS considering the coupled oxygen and laser effects

Figure 3 shows the main proposed procedures to build the kinetic model of polyamide 12 aging

involving the coupled oxygen and laser effects in SLS.

We separated the printed SLS specimens in Table 1 into two sample groups (SLS sample groups 1 and

2). Each group contains SLS samples with different polyamide 12 combinations. The objective is to ensure

that the method can derive the coefficient of the coupled oxygen and laser effects,

, for different

polyamide 12 combinations. For samples i in group 1, we performed sensitivity analysis on the modelling

degradation rates as the coupled laser and oxygen effects

O2 changes, using the basic autoxidation

model. Figure 4 presents the relationship between and

O2 for sample i.

SLS sample group 2

The proposed model

Model verification

Coefficients of aging

Aging rates with time

Basic autoxidation model FTIR spectra

Beer-Lamberts law

Actual degradation rates

Sensitivity analysis

Modelling the aging

SLS sample group 1

Sample density Oxidation time

Figure 3 Proposed procedures to build the kinetic model of polyamide 12 involving the coupled oxygen and laser-induced

aging in SLS

Figure 4 Experimental relationship between and

O2 for sample i

The experimental data suggest a second-order relationship between and

O2 in the tested operation

zone. We thus propose the following second-order correlation mapping

O2

O2 (30)

where , , and are constants for sample i. We will perform parameter identification with R-squared

regression and a full model verification in Section 3. When the modelling degradation rate equals the

actual degradation rate (section 2.2.2), the corresponding

O2 represents the actual coupled laser

and oxygen effects in SLS, defined as

O2.

Replacing with

in the basic autoxidation model, we obtain an updated oxidation model of

polyamide 12 in SLS. In this model, we define the material degradation rates as the updated modelling

degradation rates . We utilize the updated model to conduct sensitivity analysis on and the specimen

oxidation time . Figure 5 shows the experimentally identified relationship between and for sample i.

Figure 5 Experimental relationship between and for sample i

After the initial transient, the relationship between and fits an R-squared cubic polynomial, defined as

Eq. 31.

(31)

where , , and are constants.

The proposed kinetic model contains the basic autoxidation model, the coefficient of the actual coupled

laser and oxygen effects in SLS, and the relationships between the updated modelling degradation rates

and specimen oxidation time . To verify the proposed kinetic model, we apply it to the SLS sample group

2 to compare the updated modelling aging rates and the actual degradation rates .

2.4. Characteristics of the updated modelling degradation rates

The actual coupled laser and oxygen effects in SLS,

O2, and the preheating temperature are

predominant parameters in SLS affecting the material degradation rates. To understand the process further,

we use the proposed kinetic model to identify the influences of

O2 and preheating temperatures

(Table 2 and Table 3) on the updated modelling degradation rates, . These results will be analyzed in

section 3.3.

Table 3 The elementary reaction constants for thermal oxidation of polyamide 12 between 90 and 150 °C [26,27,29]

Parameter

Value

90 °C

100 °C

120 °C

140 °C

150 °C

k2 (L·mol-1·s-1)

108

108

108

108

108

k3 (L·mol-1·s-1)

1.6

2.7

7.7

19.6

30.3

k6 (s-1)

8.0×10-7

2.2×10-6

1.8×10-5

1.6×10-4

4.0×10-4

k7 (L·mol-1·s-1)

4.0×10-5

9.0×10-5

5.0×10-4

1.7×10-3

3.5×10-3

k8 (L·mol-1·s-1)

8.0×1011

8.0×1011

8.0×1011

8.0×1011

8.0×1011

k9 (L·mol-1·s-1)

5.0×1011

5.0×1011

5.0×1011

5.0×1011

5.0×1011

k10 (L·mol-1·s-1)

8.0×109

2.6×1010

6.0×1010

5.0×1010

9.5×1010

k11 (s-1)

2.0×108

2.0×108

2.0×108

2.0×108

2.0×108

k12 (s-1)

3.4×108

3.4×108

3.4×108

3.4×108

3.4×108

k13 (s-1)

3.2×108

4.7×108

7.9×108

1.2×109

1.8×109

γ1 (%)

100

95

80

55

55

γ2 (%)

100

95

80

55

55

3. Results and discussions

3.1. Comparisons between the modelling aging and the actual SLS aging rates

As introduced in section 2.2.3, we run the basic autoxidation model and get the modelling degradation

rates for each specimen i in Table 1, presented in the following section. As for the actual degradation,

Figure 6 exhibits the FTIR results of the SLS samples in Table 1, which we shall now extrapolate into

measured degradation rates . The horizontal axis is the wavenumber, and the vertical axis is the

absorbance. Our focus here is to get the absorbance differences of oxidation-related wavelengths at 1369.23,

1159.03, 1062.60, and 948.82 cm-1. Then using the Beer-Lambert’s law [15], we can calculate the

concentrations of the oxidation-related components for each sample. The differences of the concentrations

between different samples represent the different oxidation states.

(a) Polyamide 12 new powder and parts (b) Polyamide 12 parts using mixed powder (420 s)

(c) Polyamide 12 parts using mixed powder (720 s) (d) Polyamide 12 aged powder and parts

Figure 6 FTIR test results of different polyamide 12 powders and different 3D-printed part samples with different

oxidation time

Figure 7 compares FTIR curves of SLS samples at the oxidation-related wavelengths of 1369.23,

1159.03, 1062.60, and 948.82 cm-1. The diminishment or disappearance of peaks at oxidation-related

components indicates the material degradation and oxidization (Figure 7a and 7i). The peaks decrease more

when the aging time increases (Figure 7b, 7c, 7d, 7e, 7f, 7g, and 7h). As introduced in section 2.2.2, we

calculated the concentration changes (mol·L-1) of oxidation-related components for each sample during

specific aging durations, and further obtained the actual degradation rates in mol·L-1·s-1 using the Eqs.

27-28.

(a) New powder and parts using new powders (b) Part using 70% new and 30% aged powders

(c) Part using 60% new and 40% aged powders (d) Part using 50% new and 50% aged powders

(e) Part using 40% new and 60% aged powders (f) Part using 30% new and 70% aged powders

(g) Part using 20% new and 80% aged powders (h) Part using 10% new and 90% aged powders

(i) Aged powder and parts using aged powders

Figure 7 Comparison of FTIR peaks at the wavelengths of 1369.23, 1159.03, 1062.60, and 948.82 cm-1 when testing

different polyamide 12 samples

Figure 8 compares the modelling degradation rates and the actual degradation rates . Nontrivial

but unsurprising, the actual degradation rates of polyamide 12 are much larger than the modelling

degradation rates. This phenomenon exists in all samples, including those using pure new polyamide 12

powders (Figure 8a), new-aged mixed powders (Figure 8b), and pure aged powders (Figure 8c). This core

finding indicates that the coupled oxygen and laser age the material much faster than the case with oxygen

only. It is thus necessary and important to build the kinetic model of polyamide 12 aging in SLS considering

the coupled oxygen and laser effects.

(a) Parts using new polyamide 12 powders

(b) Parts using mixed polyamide 12 powders

(c) Parts using aged polyamide 12 powders

Figure 8 Comparisons between the modelling aging rates and the actual SLS aging rates for different printed samples

using polyamide 12 powders

3.2. Building the kinetic model of polyamide 12 aging in SLS considering the coupled oxygen and

laser effects

3.2.1. Determining the coefficients of the actual coupled laser and oxygen effects in SLS,

Table 4 shows the selected SLS sample group 1 and the associated time of oxidation. After performing

the sensitivity analysis using the basic autoxidation model, we conducted curve fitting between the

modelling degradation rates and the coupled laser and oxygen effects

O2 to an R-squared second-

order polynomial (Eq. 30). Figure 9 exhibits the results of sensitivity analysis and the fitting equations.

Table 4 SLS sample group 1

Sample

Time of oxidation/seconds

Parts using 100% new powders

440, 480

Parts using 70% new and 30% aged powders

420

Parts using 60% new and 40% aged powders

420

Parts using 50% new and 50% aged powders

420

Parts using 40% new and 60% aged powders

720

Parts using 30% new and 70% aged powders

420

Parts using 20% new and 80% aged powders

420

Parts using 10% new and 90% aged powders

720

Parts using 100% aged powders

440, 480

(a) 440 seconds of oxidation (part using new powders) (b) 480 seconds of oxidation (part using new powders)

(c) 420 seconds of oxidation (part using 70% new powders) (d) 420 seconds of oxidation (part using 60% new powders)

(e) 420 seconds of oxidation (part using 50% new powders) (f) 720 seconds of oxidation (part using 40% new powders)

(g) 420 seconds of oxidation (part using 30% new powders) (h) 420 seconds of oxidation (part using 20% new powders)

(i) 720 seconds of oxidation (part using 10% new powders) (j) 440 seconds of oxidation (part using aged powders)

(k) 480 seconds of oxidation (part using aged powders)

Figure 9 Sensitivity analysis and the fitting equations between and

O2 to an R-squared second-order polynomial

In each fitting equation, letting the modelling degradation rates, , equal to the actual degradation

rates , we obtain the actual coupled laser and oxygen effects in SLS,

O2, and the coefficients of

(Table 5). Here, we obtain the updated oxidation model, including the basic autoxidation model and

. The values of

indicate that the coupled laser and oxygen effects are about 4 times more than

the case with only oxygen (=1), and the laser effects are on average 4.4 times stronger than oxygen

effects on polyamide 12 degradation.

Table 5 The calculated coefficients of the coupled oxygen and laser effects,

, in the SLS process

Sample

Fitting curves between modelling degradation

rates () and the coupled oxygen and laser

effects (

O2)

The actual

degradation

rates in SLS

/mol·L-1·s-1

The actual

coupled laser and

oxygen effects in

SLS,

O2

/mol·L-1

Coefficients of

the actual

coupled laser

and oxygen

effects in SLS,

/mol·L-1

Figure 9a

μ=6.563×10-6+0.029O2-2.475(O2)2

5.105×10-5

1.804×10-3

5.010

Figure 9b

μ=6.283×10-6+0.030O2-2.338(O2)2

4.916×10-5

1.632×10-3

4.533

Figure 9c

μ=7.071×10-6+0.029O2-3.043(O2)2

4.944×10-5

1.753×10-3

4.868

Figure 9d

μ=5.353×10-6+0.031O2-3.272(O2)2

5.109×10-5

1.861×10-3

5.170

Figure 9e

μ=5.853×10-6+0.029O2-3.002(O2)2

4.228×10-5

1.453×10-3

4.037

Figure 9f

μ=5.632×10-6+0.016O2-0.578(O2)2

3.418×10-5

1.919×10-3

5.332

Figure 9g

μ=5.916×10-6+0.029O2-3.118(O2)2

4.992×10-5

1.878×10-3

5.216

Figure 9h

μ=5.840×10-6+0.029O2-3.142(O2)2

4.486×10-5

1.622×10-3

4.504

Figure 9i

μ=1.504×10-6+0.014O2-0.729(O2)2

2.532×10-5

1.622×10-3

4.505

Figure 9j

μ=3.900×10-6+0.034O2-4.761(O2)2

3.371×10-5

1.022×10-3

2.838

Figure 9k

μ=3.517×10-6+0.036O2-4.749(O2)2

3.363×10-5

9.740×10-4

2.705

3.2.2. Determining the relationship between the updated modelling degradation rates and

oxidation time

This subsection identifies the relationships between the updated modelling degradation rates and

oxidation time using the updated oxidation model. First, we conducted a sensitivity analysis on

concentration changes of oxidative components as oxidation time increases (Figure 10). The observation

is that the sample using 100% aged powders has the slowest rates of concentration changes when

seconds. This is largely due to that the aged powders develop a lot of oxidized components from the thermal

history.

Figure 10 Sensitivity analysis on concentration changes of the oxidative components as oxidation time increases using

the updated oxidation model

We divided the concentration changes by oxidation time to get degradation curves, and fit the curves

to a series of cubic-polynomial (Eq. 31). Figure 11 shows the fitting equations between the updated

modelling degradation rates and oxidation time . In the sensitivity analysis curve, the model output

goes up quickly from zero to the maximum and then goes down within seconds. The reason is that a strong

thermal impetus initiates and simultaneously accelerates the degradation reaction at a time close to zero. At

this stage, the impetus dominantly controls the reaction and continuously increases the degradation rates

until arriving at the maximum point. However, when the reaction runs normally, the basic parameters, e.g.,

initial concentrations of components, elementary reaction coefficients, laser and oxygen effects, take

control of the reaction. At this stage, the influences of the initiation impetus on degradation rates diminish

rapidly and disappear gradually.

(a) Part using 100% new powders (b) Part using 70% new powders

(c) Part using 60% new powders (d) Part using 50% new powders

(e) Part using 40% new powders (f) Part using 30% new powders

(g) Part using 20% new powders (h) Part using 10% new powders

(i) Part using 100% aged powders

Figure 11 Fitting equations between the updated modelling degradation rates and oxidation time

3.2.3. The proposed kinetic model

For different polyamide 12 powder combinations, Table 6 lists the coefficients of the actual coupled

laser and oxygen effects in SLS,

, and the fitting equations between the updated modelling

degradation rates and oxidation time . The proposed kinetic scheme of polyamide 12 aging in SLS

considering the coupled oxygen and laser effects includes the basic autoxidation model,

and fitting

equations between and . From there, we can predict the sample degradation in SLS through powder

combination and oxidation time.

Table 6 The coefficients of the actual coupled laser and oxygen effects in SLS,

, and the fitting equations between

the updated modelling degradation rates and oxidation time

Sample

/mol·L-1

The fitting equations between the updated modelling

degradation rates and oxidation time

Part using 100% new powders

4.772

= 1.268×10-4-3.015×10-7·t + 3.250×10-10·t2-1.244×10-13·t3

Part using 70% new powders

4.868

= 1.265×10-4-3.008×10-7·t + 3.246×10-10·t2-1.244×10-13·t3

Part using 60% new powders

5.170

= 1.259×10-4-2.884×10-7·t + 3.050×10-10·t2-1.155×10-13·t3

Part using 50% new powders

4.037

= 1.149×10-4-2.841×10-7·t + 3.123×10-10·t2-1.209×10-13·t3

Part using 40% new powders

5.332

= 1.228×10-4-2.908×10-7·t + 3.450×10-10·t2-1.547×10-13·t3

Part using 30% new powders

5.216

= 1.195×10-4-2.784×10-7·t + 3.263×10-10·t2-1.449×10-13·t3

Part using 20% new powders

4.504

= 1.127×10-4-2.759×10-7·t + 3.335×10-10·t2-1.513×10-13·t3

Part using 10% new powders

4.505

= 1.096×10-4-2.639×10-7·t + 3.150×10-10·t2-1.416×10-13·t3

Part using 100% aged powders

2.772

= 1.096×10-4-2.639×10-7·t + 3.150×10-10·t2-1.416×10-13·t3

Inserting the modelling related parameters of SLS sample group 2 (Table 7) into the proposed kinetic

model, we predicted the degradation rates of these samples. Figure 12 compares the predicted degradation

using the proposed kinetic model and the measured actual SLS degradation of sample group 2. Small

deviations between the predicted and the actual degradation results exist. Figure 12 presents average

deviations of 9.43% between and , respectively, exhibiting a substantial improvement compared to the

results in Figure 8. The proposed kinetic model is capable to predict the SLS degradation rates of polyamide

12 accurately.

Table 7 SLS sample group 2

Sample

Oxidation time/seconds

Parts using 100% new powders

540, 720

Parts using 70% new and 30% aged powders

720

Parts using 60% new and 40% aged powders

720

Parts using 50% new and 50% aged powders

720

Parts using 40% new and 60% aged powders

420

Parts using 30% new and 70% aged powders

720

Parts using 20% new and 80% aged powders

720

Parts using 10% new and 90% aged powders

420

Parts using 100% aged powders

540, 720

Figure 12 The comparisons between the predicted degradation rates and the actual SLS degradation rates of the SLS

sample group 2 (Parts using polyamide 12 powders of different combinations)

3.2.4. Discussions

Table 8 presents the actual SLS degradation rates from experimentation, the modelling degradation

rates from the basic autoxidation model, and the updated modelling degradation rates from the

proposed kinetic model. The modelling degradation rates have large deviations compared to the actual

SLS degradation rates , while the updated modelling degradation rates are close to . The predicted

degradations from the proposed kinetic model match on average 89.53% with the actual SLS degradation

rates , in contrast to a 34.48% accuracy from a basic autoxidation model.

Table 8 Comparisons between the actual SLS degradation rates , the modelling degradation rates from the basic

autoxidation model, and the updated modelling degradation from the proposed kinetic model

Sample

The actual SLS

degradation rates

/mol·L-1·s-1

The basic autoxidation model

The proposed kinetic model

Degradation

rates

/mol·L-1·s-1

Deviation/%

Degradation

rates

/mol·L-1·s-1

Deviation/%

Part/100% new powder/540 s

4.726×10-5

1.347×10-5

71.505

3.913×10-5

17.177

Part/100% new powder/720 s

3.021×10-5

1.023×10-5

66.129

3.174×10-5

5.054

Part/70% new powder/720 s

3.065×10-5

9.819×10-6

67.964

2.971×10-5

3.065

Part/60% new powder/720 s

3.386×10-5

9.538×10-6

71.832

2.971×10-5

10.156

Part/50% new powder/720 s

3.128×10-5

9.648×10-6

69.162

2.432×10-5

22.260

Part/40% new powder/420 s

3.4974×10-5

1.577×10-5

54.894

3.954×10-5

13.058

Part/30% new powder/720 s

3.354×10-5

9.545×10-6

71.542

2.907×10-5

13.319

Part/20% new powder/720 s

2.634×10-5

6.678×10-6

74.647

2.533×10-5

3.823

Part/10% new powder/420 s

4.100×10-5

1.560×10-5

61.943

3.554×10-5

13.311

Part/100% aged powder/540 s

2.560×10-5

1.253×10-5

51.069

2.894×10-5

13.044

Part/100% aged powder/720 s

2.395×10-5

9.568×10-6

60.045

2.372×10-5

0.936

3.3. Characteristics of the updated modelling degradation rates

3.3.1. Influences of the coupled laser and oxygen effects on

3.3.1.1. Degradation characteristics in presence of decreasing oxidations

To identify the degradation trend here, we reduce

O2 for different part samples in Table 9.

Inserting the

O2 into the proposed kinetic model, we obtained curves between the updated

modelling degradation rates and oxidation time (Figure 13). Figures 13a, 13b, and 13c are the results

for, respectively, SLS 3D-printed part using 100% new powders, part using 50%-50% new-aged powders,

and part using 100% aged powders. The curves in different colors point out the nonlinear

relationship between

O2 and the degradation rate. The black curves in Figure 13a-c are the

benchmark curves with the original

O2.

For different samples in Figure 13, when

O2 reduces, the updated modelling degradation rates

increase from zero to the maximum quickly, then decrease with time. For a specific sample (e.g., Figure

13a, the new-SLS part), the maximum of drops as

O2 decreases. The new-SLS part (Figure 13a)

always has the largest degradation rate, while the aged-SLS part (Figure 13c) has the smallest . For the

mixed (Figure 13b) and aged-SLS parts (Figure 13c), curves with

O22 (7.267×10-4 mol/L for

mixed and 4.989×10-4 mol/L for aged) and

O25 (2.907×10-4 mol/L for mixed and 1.996×10-4

mol/L for aged) result in a large drop of compared to the benchmark curves, especially at the

peak degradation points. However, further curves (curves with

O210,

O220 , and

O2100) show small changes in comparison to the curve with

O25. After about 1200 s of

oxidation (=1200 s), the rates of degradation all approach the steady state. This convergence is much

faster when the oxidation effect is reduced. In addition, when reusing powders, degradation significantly

slows down when oxidation is reduced by a factor of 5, and remains afterwards (Figure 13bc).

Table 9 The decreasing

O2

Sample

The actual

coupled laser

and oxygen

effects in SLS,

O2

/mol·L-1

O2/

2

O2/

5

O2/

10

O2/

20

O2/

50

O2

/100

Unit: mol·L-1

Part using 100%

new powders

1.718×10-3

8.589×10-4

3.435×10-4

1.718×10-4

8.589×10-5

3.435×10-5

1.718×10-5

Part using 50%

new powders

1.453×10-3

7.267×10-4

2.907×10-4

1.453×10-4

7.267×10-5

2.907×10-5

1.453×10-5

Part using 100%

aged powders

9.978×10-4

4.989×10-4

1.996×10-4

9.978×10-5

4.989×10-5

1.996×10-5

9.978×10-6

(a) Part using 100% new powders (b) Part using 50%-50% new-aged powders

(c) Part using 100% aged powders

Figure 13 Curves between the updated modelling degradation rates and oxidation time with decreasing

O2 for

different part samples

3.3.1.2. Degradation characteristics in presence of increasing oxidations

Table 10 presents the designed experiments with increasing

O2 for different part samples.

Applying the increasing

O2 to the proposed kinetic model, we obtain the curves between

the updated modelling degradation rates and oxidation time (Figure 14). Figures 14a, 14b, and 14c are

respectively for SLS 3D-printed part using 100% new powders, part using 50%-50% new-aged powders,

and part using 100% aged powders. The curves in different colors represent differently increased

O2. The black curves in Figure 14a-c are the benchmark curves with the original

O2.

In Figure 14, increases from zero to the maximum quickly, then decreases with time. For any

specific sample (e.g., Figure 14a, the new-SLS part), the maximum of rises as

O2 increases.

Having the same increasing degree for

O2 (e.g.,

O2×10), the new-SLS part always has the

largest , while the aged-SLS part has the smallest . For new, mixed, and aged-SLS parts, curves with

O2×2 and

O2×5 lead to obvious increases of . However, the other curves (curves with

O2×10,

O2×20,

O2×50,

O2×100) differ little compared to the curve with

O2×5. The result indicates that further increasing

O2 does not influence significantly.

Till 1200 s, all the curves are at or close to reaching the steady state.

Table 10 The increasing

O2

Sample

The actual

coupled laser

and oxygen

effects in SLS,

O2

/mol·L-1

O2

×2

O2

×5

O2

×10

O2

×20

O2

×50

O2

×100

Unit: mol·L-1

Part using 100%

new powders

1.718×10-3

3.435×10-3

8.589×10-3

1.718×10-2

3.435×10-2

8.589×10-2

1.718×10-1

Part using 50%

new powders

1.453×10-3

2.907×10-3

7.267×10-3

1.453×10-2

2.907×10-2

7.267×10-2

1.453×10-1

Part using 100%

aged powders

9.978×10-4

1.996×10-3

4.989×10-3

9.978×10-3

1.996×10-2

4.989×10-2

9.978×10-2

(a) Part using 100% new powders (b) Part using 50%-50% new-aged powders

(c) Part using 100% aged powders

Figure 14 Curves between the updated modelling degradation rates and oxidation time with increasing

O2 for

different part samples

3.3.1.3. Comparisons

Figure 15 compares at 1200 s for different samples to reveal material degradation rates at the steady

state. In Figure 15, the purple bars are the benchmark @1200 s data with the original

O2. When

O2 decreases (increases), the @1200 s decreases (increases) quickly first. Further decreasing

(increasing)

O2 has little effects on @1200 s.

Table 11 compares 1200 s between the original

O2 and the decreased/increased

O2 for different samples. In contrast to the case with the original σi-SLS

ol O2, 1200 s with

σi-SLS

ol O2/100 decreased by, respectively, 89.02%, 88.77%, and 81.90% for the new, mixed and aged-SLS

parts. On the other hand, 1200 s with σi-SLS

ol O2×100 increased by, respectively, 181.78%, 197.35%,

and 183.42% for the new, mixed and aged-SLS parts.

Figure 15 Comparisons of at 1200 s for different samples to compare material degradation rates at a more stable state

Table 11 Comparisons of 1200 s between the original

O2 and the decreased/increased

O2 for different

samples

Samples

Part using new powders

Part using 50%-50% new-

aged powders

Part using aged powders

The decreasing

O2

Percentages of 1200 s decreasing when

O2 decreasing

O2/100

89.02

88.77

81.9

O2/50

89.73

88.77

80.53

O2/20

87.13

86.45

88.89

O2/10

80.38

82.86

79.73

O2/5

71.96

76.27

70.54

O2/2

43.83

43.82

42.4

The increasing

O2

Percentages of 1200 s increasing when

O2 increasing

O2×2

81.41

82.13

39.87

O2×5

180.91

193.45

164.06

O2×10

183.34

198.76

183.6

O2×20

182.53

198.23

184.14

O2×50

181.13

196.76

182.41

O2×100

181.78

197.35

183.42

3.3.2. Influences of the preheating temperature on

Figure 16 presents the curves ( curves) between the updated modelling degradation rates and

oxidation time with different preheating temperatures for (a) Part using 100% new powders, (b) Part

using 50%-50% new-aged powders, and (c) Part using 100% aged powders. In Figure 16a-c, the decreased

preheating temperatures lower the curves. When at the same temperature (e.g., 150 °C, 140 °C), the

new-SLS part has the largest (Figure 16a), while the aged-SLS part has the smallest (Figure 16c). As

the preheating temperature decreases, the peaks in the curves diminish (from 160 °C to 140 °C) and

disappear gradually (from 120 °C to 90 °C). Therefore, the peaks in the curves are likely caused by

the high temperature. Besides, when the preheating temperatures are below 120 °C, are nearly zero,

indicating that a low storage temperature below 120 °C can effectively reduce material degradation.

(a) Part using 100% new powders (b) Part using 50%-50% new-aged powders

(c) Part using 100% aged powders

Figure 16 Curves between the updated modelling degradation rates and oxidation time with different preheating

temperatures for different part samples

Figure 17 shows comparisons of at 1200 s between (a) Samples with different preheating

temperatures, and (b) Preheating temperatures for different samples. At 90 °C, 1200 s approaches to

zero, leading to almost no degradation for the material at this temperature (Figure 17b). 1200 s

decreased evenly with decreasing preheating temperatures (Figure 17a). At high temperatures (150 °C –

160 °C), the differences of 1200 s between different samples are large; those differences reduce quickly

at lower temperatures below 120 °C (Figure 17b).

(a) Samples with different preheating temperatures (b) Preheating temperatures for different samples

Figure 17 Comparisons of at 1200 s (1200 s between (a) Samples with different preheating temperatures, and (b)

Preheating temperatures for different samples

4. Conclusions

In SLS, a considerable amount of expensive polyamide 12 powders remains un-sintered but reusable

after going through severely irreversible chemical degradations. The degradation originates from the

thermal energy controlled by the coupled oxygen and laser effects. Through experimentation, and by fitting

the actual SLS degradation rates to the basic autoxidation model, we obtained the coefficients of coupled

oxygen and laser effects. A further sensitivity analysis suggests the existence of a polynomial fitting

between the sample degradation rates and oxidation time. From there, we propose a new kinetic scheme for

SLS degradation of polyamide 12 composed of the basic autoxidation model, the coefficients of coupled

oxygen and laser effects, and the relationships between the sample degradation rates and oxidation time.

The new model can predict the oxidation rates of pure or mixed (different degradation levels) polyamide

12 using two easily available parameters: materials density and oxidation time. The predicted degradations

from the proposed kinetic model match on average 89.53% with the actual SLS degradation rates, in

contrast to a 34.48% accuracy from a conventional aging model. We found that the laser effects are 4-time

stronger than oxygen effects on polyamide 12 degradation. Furthermore, we identified the influences of the

coupled oxygen and laser effects in SLS and preheating temperatures on the degradation rates. The findings

provide a first-instance knowledge of quantitative material degradation related to the estimated parameters,

and insights to reduce degradation in SLS. This work established a novel effective model to obtain the

kinetic scheme of polyamide 12 degradation to aid future studies of materials degradation and reuse in the

SLS process.

Declaration of Competing 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.

Acknowledgments

This work was supported in part by National Science Foundation Award 1953155.

References

[1] C. Balemans, S.F. Looijmans, G. Grosso, M.A. Hulsen, P.D. Anderson, Numerical analysis

of the crystallization kinetics in SLS. Additive Manufacturing 33 (2020): 101126.

[2] S. Sindinger, C. Kralovec, D. Tasch, M. Schagerl, Thickness dependent anisotropy of

mechanical properties and inhomogeneous porosity characteristics in laser-sintered polyamide 12

specimens. Additive Manufacturing 33 (2020): 101141.

[3] T.D. Ngo, A. Kashani, G. Imbalzano, K.T. Nguyen, D. Hui, Additive manufacturing (3D

printing): A review of materials, methods, applications and challenges. Composites Part B:

Engineering 143 (2018): 172-196.

[4] K. Wudy, D. Drummer, Aging effects of polyamide 12 in selective laser sintering: Molecular

weight distribution and thermal properties. Additive Manufacturing 25 (2019): 1-9.

[5] K.R. Bakshi, A.V. Mulay, A review on selective laser sintering: A rapid prototyping

technology. IOSR J. Mech. Civ. Eng 4 (2016): 53-57.

[6] J. Kruth, X. Wang, T. Laoui, L. Froyen, Lasers and materials in selective laser sintering.

Assembly Automation (2003).

[7] F. Paolucci, M. van Mook, L.E. Govaert, G. Peters, Influence of post-condensation on the

crystallization kinetics of PA12: From virgin to reused powder. Polymer 175 (2019): 161-170.

[8] C. Majewski, H. Zarringhalam, N. Hopkinson, Effect of the degree of particle melt on

mechanical properties in selective laser-sintered Nylon-12 parts. Proceedings of the Institution of

Mechanical Engineers, Part B: Journal of Engineering Manufacture 222.9 (2008): 1055-1064.

[9] D. Drummer, K. Wudy, F. Kühnlein, M. Drexler, Polymer blends for selective laser sintering:

material and process requirements. Physics Procedia 39 (2012): 509-517.

[10] D. Drummer, D. Rietzel, F. Kühnlein, Development of a characterization approach for the

sintering behavior of new thermoplastics for selective laser sintering. Physics Procedia 5 (2010):

533-542.

[11] M. Schmid, A. Amado, K. Wegener, Polymer powders for selective laser sintering (SLS).

AIP Conference proceedings 1664 (2015).

[12] P. Chen, M. Tang, W. Zhu, L. Yang, S. Wen, C. Yan, Z. Ji, H. Nan, Y. Shi, Systematical

mechanism of Polyamide-12 aging and its micro-structural evolution during laser sintering.

Polymer Testing 67 (2018): 370-379.

[13] S. Dadbakhsh, L. Verbelen, O. Verkinderen, D. Strobbe, P. Van Puyvelde, J. Kruth, Effect

of PA12 powder reuse on coalescence behaviour and microstructure of SLS parts. European

Polymer Journal 92 (2017): 250-262.

[14] K. Dotchev, W. Yusoff, Recycling of polyamide 12 based powders in the laser sintering

process. Rapid Prototyping Journal (2009).

[15] C. El-Mazry, M.B. Hassine, O. Correc, X. Colin, Thermal oxidation kinetics of additive free

polyamide 6-6. Polymer degradation and stability 98.1 (2013): 22-36.

[16] D. Drummer, K. Wudy, M. Drexler, Modelling of the aging behavior of polyamide 12

powder during laser melting process. AIP Conference Proceedings 1664 (2015).

[17] T.J. Gornet, K.R. Davis, T.L. Starr, K.M. Mulloy, Characterization of selective laser

sintering materials to determine process stability. International Solid Freeform Fabrication

Symposium (2002): 546-553.

[18] H. Zarringhalam, N. Hopkinson, N.F. Kamperman, J.J. De Vlieger, Effects of processing on

microstructure and properties of SLS Nylon 12. Materials Science and Engineering: A 435

(2006): 172-180.

[19] L. Wang, A. Kiziltas, D.F. Mielewski, E.C. Lee, D.J. Gardner, Closed-loop recycling of

polyamide12 powder from selective laser sintering into sustainable composites. Journal of

Cleaner Production 195 (2018): 765-772.

[20] L. Feng, Y. Wang, Q. Wei, PA12 Powder Recycled from SLS for FDM. Polymers 11.4

(2019): 727.

[21] T.T. Diller, M. Yuan, D.L. Bourell, J.J. Beaman, Thermal model and measurements of

polymer laser sintering. Rapid Prototyping Journal (2015).

[22] M. Yuan, T.T. Diller, D. Bourell, J. Beaman, Thermal conductivity of polyamide 12 powder

for use in laser sintering. Rapid Prototyping Journal (2013).

[23] S. Bernard, L. Youinou, P. Gillard, MIE determination and thermal degradation study of

PA12 polymer powder used for laser sintering. Journal of Loss Prevention in the Process

Industries 26.6 (2013): 1493-1500.

[24] K.T. Gillen, J. Wise, R.L. Clough, General solution for the basic autoxidation scheme.

Polymer Degradation and Stability 47.1 (1995): 149-161.

[25] L.M. Rincon-Rubio, B. Fayolle, L. Audouin, J. Verdu, A general solution of the closed-loop

kinetic scheme for the thermal oxidation of polypropylene. Polymer Degradation and Stability

74.1 (2001): 177-188.

[26] X. Colin, B. Fayolle, L. Audouin, J. Verdu, About a quasi-universal character of

unstabilised polyethylene thermal oxidation kinetics. Polymer Degradation and Stability 80.1

(2003): 67-74.

[27] X. Colin, L. Audouin, J. Verdu, Determination of thermal oxidation rate constants by an

inverse method. Application to polyethylene. Polymer Degradation and Stability 86.2 (2004):

309-321.

[28] S. Laun, H. Pasch, N. Longiéras, C. Degoulet, Molar mass analysis of polyamides-11 and-

12 by size exclusion chromatography in HFiP. Polymer 49.21 (2008): 4502-4509.

[29] N. Khelidj, X. Colin, L. Audouin, J. Verdu, C. Monchy-Leroy, V. Prunier, Oxidation of

polyethylene under irradiation at low temperature and low dose rate. Part II. Low temperature

thermal oxidation. Polymer degradation and stability 91.7 (2006): 1598-1605.