Evaluation of Tensile Stress Relaxation of Selective Laser Sintering of PA2200 Material using the Maxwell-Wiechert Model

Powder properties		Value	Unit	Test Standard
Medium grain size		60	μm	-
Density of ubound powder		0.435 – 0.445	g/cm³	DIN 53466
Density of sintered powder		0.9 – 0.95	g/cm³	EOS - Method
Mechanical Properties		Value	Unit	Test Standard
Flexural modulus, 23°C		1500	MPa	ISO 178
Flexural strength		58	MPa	ISO 178
Izod impact notched, 23°C		4.4	kJ/m²	ISO 180/1A
Izod impact unnotched, 23°C		32.8	kJ/m²	ISO 180/1U
Shore D hardness (15 s)		75	------	ISO 868
Ball indentation hardness		78	MPa	ISO 2039-1
3D Data		Value	Unit	Test Standard
Tensile modulus	X-direction	700	MPa	ISO 527-1/2
		Y-direction	1700
		Z-direction	1650
		X-direction	48
Tensile strength	Y-direction	48
		Z-direction	47
Strain at break	X-direction	24	%	ISO 527-1/2
Charpy impact strength (+23°C)	X-direction	53	kJ/m²	ISO 179/1eU
Charpy notched impact strength (+23°C)	X-direction	4.8	kJ/m²	ISO 179/1eA
Thermal conductivity	X-direction	0.144	W/(mK)	DIN 52616
	Y-direction	0.144
	Z-direction	0.127

Test specimens: a) dimensions, b) STL saving, c) print orientation

Tab. 2.

Values of technological parameters

E_d		P_d	L_t
0.056 J/mm²	0.076 J/mm²	0°, 45°, 90°	0.1 mm
P = 21 W	P=22 W
v = 2500 mm/s	v = 1970 mm/s

Mechanical analogy of the Maxwell-Wiechert model [5,13]

Appearance of samples during stress relaxation tests

Stress relaxation curves for PA2200 material; $E_{d}^{56}$ : a) $E_{d}^{56} - P_{d}^{0}$ , b) $E_{d}^{56} - P_{d}^{45}$ , c) $E_{d}^{56} - P_{d}^{90}$

Stress relaxation curves for PA2200 material: d) $E_{d}^{76} - P_{d}^{0}$ , e) $E_{d}^{76} - P_{d}^{45}$ , f) $E_{d}^{76} - P_{d}^{90}$

Example of a Maxwell-Wiechert model fit to experimental curves: a) $E_{d}^{56} - P_{d}^{0} - 1$ , b) $E_{d}^{76} - P_{d}^{0} - 1$

Tab. 3.

Maxwell-Wichert model parameters and fit coefficients; $E_{d}^{56}$

Lp.	σ₀, MPa	σ₁, MPa	σ₂, MPa	t₁, s	t₂, s	Chi²	R₂
$P_{d}^{0}$
1	7.8	0.9	0.8	11	232	0.000390	0.9942
2	8.4	0.7	0.8	10	252	0.000299	0.9945
3	8.4	0.7	0.8	10	239	0.000314	0.9947
4	7.9	0.9	0.9	11	233	0.000403	0.9947
5	7.8	0.8	0.9	11	241	0.000369	0.9948
6	8.7	0.8	0.8	11	252	0.000348	0.9942
7	8.5	0.8	0.7	11	247	0.000337	0.9937
8	8.2	0.7	0.7	11	251	0.000267	0.9941
9	8.3	0.7	0.8	11	255	0.000299	0.9949
10	8.0	0.7	0.7	11	240	0.000309	0.9938
$\bar{x}$	8.2	0.8	0.8	11	244	0.000334	0.9944
SD	0.3	0.1	0.1	0.3	8	0.000044	0.0004
$P_{d}^{45}$
1	8.6	0.9	1.0	12	243	0.000445	0.9951
2	7.9	0.9	0.9	11	241	0.000410	0.9944
3	6.3	1.0	1.2	12	263	0.000544	0.9958
4	5.8	1.0	1.0	12	249	0.000512	0.9944
5	8.1	0.7	0.7	11	267	0.000279	0.9943
6	7.6	0.7	0.7	11	259	0.000304	0.9941
7	7.7	0.7	0.7	11	252	0.000332	0.9936
8	7.0	0.7	0.7	10	264	0.000326	0.9930
9	7.9	0.7	0.8	11	258	0.000292	0.9947
10	7.4	0.7	0.7	10	249	0.000264	0.9943
$\bar{x}$	7.4	0.8	0.8	11	255	0.000371	0.9944
SD	0.8	0.1	0.2	1	9	0.000101	0.0008
$P_{d}^{90}$
1	8.4	0.9	0.9	12	257	0.000421	0.9948
2	8.0	0.9	0.9	11	245	0.000424	0.9945
3	7.9	0.9	0.9	11	245	0.000433	0.9945
4	8.3	0.9	0.9	12	242	0.000393	0.9947
5	8.3	0.9	0.9	11	245	0.000408	0.9944
6	7.7	0.8	0.9	12	262	0.000367	0.9952
7	7.9	0.8	0.9	12	253	0.000369	0.9954
8	7.7	0.8	0.8	11	260	0.000364	0.9944
9	7.7	0.8	0.9	12	262	0.000353	0.9954
10	8.0	0.8	0.9	12	268	0.000391	0.9952
$\bar{x}$	8.0	0.8	0.9	12	254	0.000392	0.9948
SD	0.3	0.04	0.03	0.3	9	0.000028	0.0004

Tab. 4.

Maxwell-Wichert model parameters and fit coefficients; $E_{d}^{76}$

Lp.	σ₀, MPa	σ₁, MPa	σ₂, MPa	t₁, s	t₂, s	Chi²	R₂
$P_{d}^{0}$
1	7.9	0.9	1.1	13	255	0.000464	0.9960
2	6.7	0.8	0.8	12	251	0.000377	0.9945
3	7.6	0.9	1.0	12	249	0.000404	0.9954
4	7.0	0.8	0.9	11	242	0.000382	0.9950
5	7.4	0.9	0.9	12	243	0.000425	0.9947
6	7.5	0.9	1.0	12	248	0.000412	0.9956
7	7.5	0.9	1.0	12	251	0.000439	0.9952
8	7.7	0.9	1.0	12	245	0.000434	0.9953
9	7.4	0.9	1.0	11	244	0.000402	0.9952
10	7.7	0.9	1.0	13	246	0.000434	0.9953
$\bar{x}$	7.4	0.9	1.0	12	247	0.000418	0.9952
SD	0.4	0.03	0.1	1	4	0.000027	0.0004
$P_{d}^{45}$
1	7.8	0.9	1.0	9	209	0.000264	0.9971
2	7.1	0.8	0.9	14	337	0.000558	0.9917
3	8.1	0.9	1.0	8	193	0.000226	0.9974
4	7.7	0.9	0.9	14	314	0.000579	0.9925
5	7.9	0.9	1.0	9	224	0.000252	0.9970
6	7.1	0.8	0.8	9	182	0.000303	0.9953
7	6.7	0.8	0.9	13	330	0.000343	0.9945
8	7.1	0.8	1.0	17	464	0.000635	0.9908
9	7.4	0.8	1.0	12	264	0.000395	0.9953
10	7.2	0.8	1.0	12	257	0.000394	0.9952
$\bar{x}$	7.4	0.8	0.9	12	277	0.000395	0.9947
SD	0.4	0.04	0.1	3	86	0.000147	0.0023
$P_{d}^{90}$
1	7.2	0.8	0.9	12	258	0.000373	0.9949
2	7.9	0.9	1.0	11	252	0.000415	0.9953
3	7.9	0.9	1.0	12	253	0.000446	0.9952
4	7.9	0.9	1.0	12	253	0.000430	0.9954
5	7.5	0.9	1.0	12	244	0.000415	0.9953
6	7.4	0.9	1.0	13	239	0.000444	0.9951
7	8.1	0.9	1.0	12	250	0.000458	0.9953
8	7.6	0.9	0.9	11	251	0.000414	0.9949
9	7.6	0.9	1.0	12	253	0.000430	0.9951
10	7.9	1.0	1.0	12	248	0.000482	0.9951
$\bar{x}$	7.7	0.9	1.0	12	250	0.000431	0.9952
SD	0.3	0.04	0.04	0.4	5	0.000029	0.0001

Moduli of elasticity for PA 2200 material

Dynamic viscosity coefficients for PA 2200 material

Tab. 5.

Percentage of stress drop in PA2200 material

Rσ, %
$E_{d}^{56}$
P_d	₀°	45°	90°
$\bar{x}$	20.98	23.85	22.61
SD	1.86	4.86	0.56
$E_{d}^{76}$
$\bar{x}$	24.5	23.6	24.1
SD	0.4	0.5	0.4

References

Authors

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Articles in this issue

DOI: https://doi.org/10.2478/ama-2025-0036 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088

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Language: English

Page range: 292 - 299

Submitted on: Dec 16, 2024

Accepted on: Apr 14, 2025

Published on: Jun 30, 2025

Published by: Bialystok University of Technology

In partnership with: Paradigm Publishing Services

Keywords:

3D printing,

stress relaxation,

Maxwell-Wiechert model,

SLS

Related subjects:

Engineering,

Mechanical engineering,

Mechanics,

Bioengineering and biomedical engineering,

Biomechanics,

Civil engineering,

Environmental engineering

© 2025 Wiktor SZOT, Mateusz RUDNIK, Paweł SZCZYGIEŁ, Natalia KOWALSKA, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2025): Issue 2 (June 2025)

Evaluation of Tensile Stress Relaxation of Selective Laser Sintering of PA2200 Material using the Maxwell-Wiechert Model

Figures & Tables

Tab. 1.

Fig. 1.

Fig. 2.

Tab. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

Tab. 3.

Tab. 4.

Fig. 8.

Fig. 9.

Tab. 5.

Paradigm

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