Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2025.54.0001 Acta Polytechnica CTU Proceedings 54:1–7, 2025 © 2025 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague NUMERICAL VERIFICATION OF FRACTURE TOUGHNESS VALUES FOR VERY THIN 3D PRINTED POLYAMIDE SAMPLES Petr Bočan∗, Aleš Jíra Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague 6, Czech Republic ∗ corresponding author: petr.bocan@fsv.cvut.cz Abstract. This researche presents an experimental and numerical analysis of the mechanical properties of very thin polyamide (PA12) samples fabricated by 3D printing with selective laser sintering (SLS). The research methodology focuses on testing mechanical properties such as fracture toughness and simple tensile on PA12 samples ranging in size from 0.50 mm to 2.00 mm, which were then subjected to numerical analysis replicating the experiment. Significant differences between the experimental data and the numerical analysis were found, mainly due to the choice of material model and the selection of inappropriate material parameters. With the numerical analysis, these parameters were appropriately set up and the results of the numerical analysis began to agree more closely with the experimental data. Keywords: 3D printing, polyamide PA12, fracture toughness experiment, simple tensile experiment, numerical analysis. 1. Introduction Currently, 3D printing technology is one of the most advanced methods in additive manufacturing, with widespread use across various industries. This tech- nology makes it possible to create more complex struc- tures, which leads to fostering numerous innovations, making it a highly researched area. In my previous project [1], I investigated the frac- ture toughness of very thin polyamide (PA12) samples produced using SLS (Selective Laser Sintering) 3D printing. The experiment was designed following a rel- evant standard, which determined the geometry of the samples, the experimental procedure, and the final calculation of fracture toughness. The experiment were carried out on samples with widths ranging from 0.50 mm to 2.00 mm. To account for the ortotrophy of 3D printed samples, the print orientation was varied, with layers printed either perpendicular or parallel to the anticipated crack propagation. A more detailed description of the experiment and its findings can be found in Section 3.1. Another study [2] also demon- strated the influence of thickness in a simple tensile test, which is more described in Section 3.2. This project was further supplemented by a numer- ical analysis conducted using preprocessor GiD and then calculated in ATENA software [3]. The geometry of the numerical model copied that of the experimental samples, and a basic material model was established. The load was defined by deformation in form of dis- placement. The PA12 datasheet [4] provided only fundamental mechanical properties, such as Young’s modulus, tensile strength, and elongation at break. Therefore, additional mechanical properties, such as compressive strength and fracture energy from other experiments, were incorporated into the numerical analysis. Unfortunately, as shown in Figure 1, signif- 0.0 0.5 1.0 1.5 Distance [mm] 0 10 20 30 40 Fo rc e [N ] SAMPLE 2 - 0.50 mm 0.0 0.5 1.0 1.5 2.0 2.5 Distance [mm] 0 100 200 300 400 Fo rc e [N ] SAMPLE 2 - 2.00 mm Figure 1. Comparison of numerical analysis and experimental data, where the blue curve is the ex- perimental data, orange curve is the linear numerical model and green curve is the quadratic numerical model [1]. icant differences emerged between the experimental and numerical analysis results. These significant deviations led to a more detailed 1 https://doi.org/10.14311/APP.2025.54.0001 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en Petr Bočan, Aleš Jíra Acta Polytechnica CTU Proceedings investigation into the numerical analysis to identify possible sources of error. The diagrams reveal no match between the linear part of the experimental data and the numerical model, suggesting that the main problem may stem from the chosen material model. In the case of thin samples, the mechanical properties given in the data sheet are insufficient and the values may vary. As a result, a simple tensile experiment was per- formed on thin PA12 samples to describe their be- havior in the linear region. This experiment enabled the determination of Young’s modulus and tensile strength for thin samples, which were then applied to the numerical model under simple tensile loading. 2. Material and method of manufacture PA12 (Nylon 12) material was used in my experi- ment produced by SLS (Selective Laser Sintering) 3D printing technology. Nylons are part of the thermo- plastic polymer family and also they are referred to as polyamides (PA) because of their repeating units connected by amide bonds. There are numerous sub- types with varying crystal structures and material properties, including Nylon 6, Nylon 12, and Nylon 66, among others [5]. One of the popular additive man- ufacturing techniques is Powder Bed Fusion (PBF), also known as SLS. This method is widely used for printing metals and polyamide components by fusing powder particles layer by layer using a high-energy heat source. Today, 3D printing technologies are extensively used for additive manufacturing in various industries. How- ever, SLS technology presents certain challenges, es- pecially when printing thin samples. One of the main weaknesses is the inadequate bonding of powder par- ticles, and another issue is the inconsistent sample width. Poorly bonded powder particles tend to fall off during handling, which reduces the sample width and weakens its load capacity, ultimately affecting fundamental mechanical properties like the modulus of elasticity. These irregularities can significantly re- duce specimen width, influencing the experimental results and subsequently influencing the appropriate choice of material properties in numerical calculation. 3. Experimental part Two types of experiments were designed to verify the results of the numerical analysis. First, I started with an experiment dealing with fracture toughness [1], and then I supplemented the research with a simple tensile experiment. Both experiments were conducted on specimens with widths ranging from 0.50 mm to 2.00 mm. The geometries of the specimens were de- signed according to the relevant standard. A Mark 10 load press was used for loading in both experiments. The fracture toughness experiment was supplemented Figure 2. The geometries of specimens for fracture toughness experiment according to EN ISO 12737 [6]. Dimensions are given in millimetres. with 3D macro DIC to monitor crack propagation and crack length readings. 3.1. Fracture toughness experiment The fracture toughness experiment was carried out according to EN ISO 1273 [6]. With minor modifica- tions, the geometry of the specimens, the experiment procedure, and the final calculation of the fracture toughness value were taken from the standard. In the last research [1], I investigated the fracture toughness of two specimen geometries as shown in the Figure 2. The calculation of the fracture toughness value KQ according to the standard EN ISO 1273 [6] is given in the Equation 1. KQ = FQ B √ W ∗ f(a/W ), (1) where FQ is the force determine from the experiment data, B is the sample thickness, W is the length of a ligament. An essential parameter in the calculation is the geometric factor f(a/W ) shown in Equation 2, which is a dimensionless function of a/W , where a is the length of the crack. 2 vol. 54/2025 Numerical verification of fracture toughness values . . . GSEducationalVersion Pr in t d ir ec tio n Pr in t d ir ec tio n Pr in t d ir ec tio n Pr in t d ir ec tio n H V Vertical printed sample Horizontal printed sample Vertical printed sample Horizontal printed sample P ri nt o ri en ta ti on P ri nt o ri en ta ti on Horizontal printed sample Vertical printed sample Figure 3. Demonstration of the use of orthotropy using different printing direction [1]. f(a/W ) = (2 + a/W ) ∗ [0, 886 + 4, 64(a/W ) − 13, 32(a/W )2 + 14, 72(a/W )3 − 5, 6(a/W )4]/(1 − a/W ) 2 3 . (2) The orthotropy of the material was accounted for by different printing directions (hereafter referred to as H and V). Horizontally (H) printed specimens had in- dividual layers printed perpendicular to the expected crack propagation, while vertically (V) printed spec- imens had layers parallel to the expected crack. Or- thotropy is a material property, where the material has different properties in perpendicular directions. This property is typical for composite materials. Figure 3 shows a schematic of the proposed printing direction. To refine the adequacy of these results, the fracture toughness values of the PA12 material were deter- mined in other researches. J. Schneider and S. Ku- mar [7] investigated the influence of ligament length (10, 15, and 20 mm) on fracture behavior. Their study used test samples of 1 mm thick subjected to three-point bending tests. The results demonstrated a clear dependence of fracture toughness KIC on lig- ament length, with measured values ranging from 3.7–4.5 MPa √ m. A. Salazar [8] further examined the effect of three distinct temperature conditions on frac- ture behavior, reporting fracture toughness values in the range of 2.7–3.2 MPa √ m. D. I. Stoia et al. [9] focused on the influence of different printing orienta- tions and processing energy levels. Their experiments resulted in fracture toughness values ranging from 0.8–2.2 MPa √ m. In summarizing the results of other experiments, the fracture toughness value for PA12 material was around the values 0.8–4.5 MPa √ m [7–9]. Figure 4 showing the average fracture toughness KQ value for each sample thickness. For the hori- zontally printed samples with widths of 0.50 mm and 0.75 mm, significant variations in the values were ob- served, leading to unstable values in results. However, from a certain sample thickness onward, the values became more consistent and began to increase with specimen thickness. The values of the horizontally printed samples ranged from 1.4–2.6 MPa √ m. In con- trast, for the vertically printed specimens, the fracture toughness values around 1 MPa √ m did not increase 0.50 0.75 1.00 1.25 1.50 2.00 Sample width B [mm] 1.0 1.5 2.0 2.5 3.0 Fr ac tu re to ug hn es s K Q [M Pa *m 1/ 2 ] Horizontal printed samples SAMPLE 2 SAMPLE 3 0.50 0.75 1.00 1.25 1.50 2.00 Sample width B [mm] 0.5 1.0 1.5 Fr ac tu re to ug hn es s K Q [M Pa *m 1/ 2 ] Vertical printed samples SAMPLE 2 SAMPLE 3 Figure 4. Final fracture toughness values for different print thicknesses and orientations [1]. with thickness, remaining relatively constant through- out the tests. 3.2. Tensile experiment A tensile experiment was conducted by EN ISO 527-1,2 standards [10, 11]. The primary objective of this exper- iment was to determine the ultimate tensile strength of very thin specimens. Additionally, the experiment aimed to closely examine the linear behavior of thin samples under simple tensile loading. The geome- try of the specimens, as specified by the standard, is depicted in Figure 5. The orthotropy of the material was considered by varying the print orientation, as was done in the fracture toughness experiment. Vertically printed specimens had layers oriented parallel to the tensile load, while horizontally printed specimens had lay- ers perpendicular to the load. The thickness of each printed layer was set to 0.100 mm. Figure 6 provides a schematic representation of the sample printing pro- cess for both print orientations. The small number of samples in the case of 0.50 mm thick samples is due to the heavy handling during the experiment and sample cleaning, and therefore the results for this thickness cannot be considered rele- vant. The same applies to the 1.25 mm thick samples where only three samples were printed. However, for other thicknesses, an adequate number of samples 3 Petr Bočan, Aleš Jíra Acta Polytechnica CTU Proceedings Figure 5. Geometry of the specimen used for the simple tensile experiment with variable widths from 0.50 mm to 2.00 mm. GSEducationalVersion Pr in t d ir ec tio n Pr in t d ir ec tio n Pr in t d ir ec tio n Pr in t d ir ec tio n H V Vertical printed sample Horizontal printed sample Vertical printed sample Horizontal printed sample P ri nt o ri en ta ti on P ri nt o ri en ta ti on Horizontal printed sample Vertical printed sample Figure 6. Samples print direction for horizontal and vertical samples. were tested, allowing their results to be considered valid. In the technical data of PA12 [4], the tensile strength is given as 41 MPa, where it is not speci- fied at which thicknesses or at which print orientation it was found. Therefore, it was necessary to obtain the tensile strength values from other experiments, where the print orientation and thinner samples were my area of interest to search. The studies showed that the orientation of the print and the thickness of the sam- ple are the main factors in the tensile strength values. The Slager study [12] examined different print orienta- tions and thicknesses of the sample, where horizontally printed samples of 0.8 mm ranging around the tensile strength value of 20.5 MPa, for vertically printed sam- ples it was around 27.8 MPa. Sindinger [13] showed a large increase in the value with increasing thickness, where the values for horizontally printed samples were around 25–42 MPa and the values for vertically printed samples were around 26–45 MPa. Other studies have shown that tensile strength is not as much affected by the orientation of the print with increasing thick- ness [12–15]. The experiment revealed notable differences be- tween vertically and horizontally printed specimens, particularly in the maximum load at which the spec- Samples widths Tensile strength [mm] [MPa] 0.50 25.30 ± 0.06 0.75 22.61 ± 1.55 1.00 28.26 ± 1.87 1.25 32.51 ± 1.19 1.50 32.48 ± 0.97 2.00 34.24 ± 2.88 Table 1. Tensile strength for the vertically print samples [2]. Samples widths Tensile strength [mm] [MPa] 0.50 – 0.75 11.76 ± 1.04 1.00 21.29 ± 0.95 1.25 – 1.50 21.16 ± 2.62 2.00 20.07 ± 1.45 Table 2. Tensile strength for the horizontally print samples [2]. imens fractured, as shown in Figure 7. From these measurement data was calculated the ultimate tensile strength of each specimen width. The ultimate tensile strength for each specimens were calculated as: ft = Fmax A0 , (3) where ft is the tensile strength, Fmax is the maximal force from experiment data and A0 is the cross-section area measured for each samples. Tables 1 and 2 present the tensile strength results for each specimen width in both print directions. Values are not provided for horizontally printed specimens with widths of 0.50 mm and 1.25 mm due to issues with handling during the experiment and the insufficient number of specimens tested. As expected, the tensile strength values for verti- cally printed samples were higher compared to those for horizontally printed samples. This is because ver- tically printed specimens have layers oriented parallel to the applied load. Conversely, horizontally printed specimens have layers perpendicular to the load, mak- ing them more susceptible to breaking with less stress. Anyway, the PA12 technical datasheets [4] specify a tensile strength of 41 MPa, which significantly ex- ceeds the maximum value observed in this experiment. This discrepancy highlights that the manufacturer’s certified values may not be applicable for very thin specimens, emphasizing the need for careful consider- ation of material properties in such cases. 4 vol. 54/2025 Numerical verification of fracture toughness values . . . 0 1 2 3 Distance [mm] 0 20 40 60 Lo ad [N ] Thickness 0.50 mm 0 1 2 3 4 5 Distance [mm] 0 30 60 90 120 150 Lo ad [N ] Thickness 1.00 mm 0 1 2 3 4 Distance [mm] 0 50 100 150 200 250 Lo ad [N ] Thickness 1.50 mm 0 1 2 3 4 5 Distance [mm] 0 50 100 150 200 250 300 350 Lo ad [N ] Thickness 2.00 mm Figure 7. Diagrams of Load – Distance values for specimens with widths 0.50, 1.00, 1.50, 2.00 mm. Blue curves indicate samples printed in the horizontal di- rection, red curves indicate samples printed in the vertical direction [2]. 4. Numerical analysis The numerical model was developed using GiD 16.0.6 software, which serves as a preprocessor for numeri- cal analysis. Finite element analysis (FEA) was per- formed with ATENA software [3], typically used for the nonlinear analysis of concrete structures but adapt- able for other materials when the appropriate material model is selected. This software excels in numerical simulation experiments, providing detailed insights into crack progression and maximum load capacity before failure. As mentioned in the introduction, the manufac- turer provides limited mechanical parameter informa- tion for PA12. The values given in the datasheets include Young’s modulus E = 1.47 GPa, ultimate ten- sile strength ft,u = 41 MPa and elongation at break ϵu = 0.13 [4]. Consequently, the fracture energy Gf and Poisson’s ration µ had to be determine through additional experiments. The material properties used in the FEA for the previous project [1] are given in Table 3. Material properties PA12 material Young’s modulus E [GPa] 1.47 Poisson’s Ratio µ [-] 0.4 Density ρ [kg m−3] 1010 Thermal expansion α [K−1] 10−12 Tension Strength ft [MPa] 41 Fracture Energy Gf [kN m−1] 7 Table 3. Material properties used in the calculation for previous research [1]. These material properties showed large differences in the FEA results compared to experimental data. It may happen because of the wrong selection of the material model and Young’s modulus. Thus, a large parametric study of the simple tensile calculation on the value of effective Young’s modulus was per- formed. The calculation showed the value of effective Young’s modulus around 250 MPa, which is 6 times lower than stated by the manufacturer. Also, the material model was set with elasto-plastic behavior using Cementitious2 − User. 5. Conclusions Previous research [1] investigated the fracture tough- ness of very thin PA12 samples, involving both ex- perimental and numerical parts. The experimental phase included extensive testing on sample thicknesses ranging from 0.50 mm to 2.00 mm and incorporated orthotropy by varying the printing directions. Numer- ical analysis was then conducted using ATENA soft- ware [3] to simulate the experiments, but significant discrepancies were observed between the numerical predictions and experimental data. These differences were likely due to an inadequate material model and the selection of inappropriate 5 Petr Bočan, Aleš Jíra Acta Polytechnica CTU Proceedings material parameters. The material model used had a quasi-brittle behavior, which was not suitable for PA12, as this material exhibits elasto-plastic behavior. It is well established that for thin samples produced via SLS powder technology, manufacturer specified material properties are not directly applicable, and effective material properties for these thin samples must be determined experimentally. The manufacturer’s datasheet provide limited infor- mation on the mechanical properties of PA12, such as Young’s modulus and tensile strength, which can be determined by a simple tensile test. Therefore, this research focused on performing a simple tensile exper- iment to analyze the linear behavior of the samples under load, which allowed the determination of effec- tive Young’s modulus and ultimate tensile strength for these thin samples. Again, orthotropy with different printing directions was considered. As with the fracture toughness tests, it was found that the printing direction affects the material’s re- sponse to load. Specifically, samples with layers printed parallel to the load direction showed better performance. The experiments demonstrated increas- ing values with specimen thickness and highlighted substantial differences between the manufacturer’s pro- vided material properties and those obtained through experimentation, as summarized in Table 4. This underscores the fact that standardized parameters cannot be taken into account for very thin samples. Material Data-sheets Experiment properties Young’s modulus 1.47 0.20–0.26 E [GPa] Tension Strength 41 22–35 ft [MPa] Table 4. The comparison of material properties pro- vided by the manufacturer’s datasheet with the exper- imental results for vertically printed samples. The results were verified through Finite Element Analysis (FEA) using ATENA software [3]. Initially, a study was conducted to determine the effective Young’s modulus, which was found to be Eeff = 250 MPa. This value aligned with Young’s modulus obtained from experimental data. Subsequently, the material model was modified to an elasto-plastic model using the Cementitious2 − User option. These ad- justments to the material properties and model proved effective, as the numerical analysis results began to closely match the experimental values. Figure 8 shows the result for thicknesses 0.50, 1.00, 1.50 and 2.00 mm, which can be seen there is pretty close agreement be- tween experimental data and FEA results. The small deviations between the experimental data and FEA are due to the choice of one typical value of effective Young’s modulus. 0 1 2 3 4 5 Distance [mm] 0 10 20 30 40 50 60 70 Lo ad [N ] Thickness 0.50 mm Experimental data FEA calculation 0 1 2 3 4 5 Distance [mm] 0 50 100 150 Lo ad [N ] Thickness 1.00 mm Experimental data FEA calculation 0 1 2 3 4 5 Distance [mm] 0 50 100 150 200 250 Lo ad [N ] Thickness 1.50 mm Experimental data FEA calculation 0 1 2 3 4 5 Distance [mm] 0 50 100 150 200 250 300 350 Lo ad [N ] Thickness 2.00 mm Experimental data FEA calculation Figure 8. Comparison of experimental data of simple tensile and FEA calculation using elasto-plastic mate- rial material model and the effective Young’s modulus Eeff = 250 MPa in the calculation. 6 vol. 54/2025 Numerical verification of fracture toughness values . . . Acknowledgements The financial support from Czech Science Foundation (project No. 23-04971S) and Czech Technical University in Prague (SGS project No. SGS23/152/OHK1/3T/11) is gratefully acknowledged. References [1] P. Bočan. Experimental verification of the influence of thickness on 3D printed samples on fracture toughness parameters. Master’s thesis, Czech Technical University in Prague, Department of Mechanics, Prague, 2024. [2] P. Bočan, A. Jíra. Determination of mechanical properties of very thin 3D-printed specimens for numerical analysis of tensile strength and fracture toughness. Acta Polytechnica 65(3):263–275, 2025. https://doi.org/10.14311/AP.2025.65.0263 [3] Červenka, J., L. Jendele, V. Červenka. 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Additive Manufacturing 33:101141, 2020. https://doi.org/10.1016/j.addma.2020.101141 [14] N. Lammers, M. Kersemans, I. De Baere, W. Van Paepegem. On the visco-elasto-plastic response of additively manufactured polyamide-12 (PA-12) through selective laser sintering. Polymer Testing 57:149–155, 2017. https: //doi.org/10.1016/j.polymertesting.2016.11.032 [15] A. G. Rodríguez, E. E. Mora, M. A. Velasco, C. A. N. Tovar. Mechanical properties of polyamide 12 manufactured by means of SLS: Influence of wall thickness and build direction. Materials Research Express 10(10):105304, 2023. https://doi.org/10.1088/2053-1591/acf6f7 7 https://doi.org/10.14311/AP.2025.65.0263 https://www.cervenka.cz/ https://doi.org/10.1515/polyeng-2020-0302 https://doi.org/10.1016/j.polymertesting.2020.106357 https://doi.org/10.1016/j.polymertesting.2020.106357 https://doi.org/10.1016/j.eurpolymj.2014.07.016 https://doi.org/10.1016/j.tafmec.2020.102497 https://doi.org/10.3390/polym16162241 https://doi.org/10.1016/j.addma.2020.101141 https://doi.org/10.1016/j.polymertesting.2016.11.032 https://doi.org/10.1016/j.polymertesting.2016.11.032 https://doi.org/10.1088/2053-1591/acf6f7 Acta Polytechnica CTU Proceedings 54:1–7, 2025 1 Introduction 2 Material and method of manufacture 3 Experimental part 3.1 Fracture toughness experiment 3.2 Tensile experiment 4 Numerical analysis 5 Conclusions Acknowledgements References