Evaluating 3D Printing Parameters of an Elastomeric Resin for Higher Stretchability and Strength Using the Analytic Hierarchy Process and Technique for Order of Preference by Similarity to Ideal Solution ^†

Abstract

The fast progress of 3D printing technology has resulted in the creation of innovative materials, such as elastic resins, broadening the field of applications in various sectors. This paper investigates the effect of printing parameters on the strength and elongation of the final part, as well as optimizing elastic resin 3D printing processes using the Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) analyses. In this analysis, the printing parameters post-curing time, exposure time, aging conditions, rotation direction, rest time after lift, photoinitiator effect, and aging time are considered criteria. The report finishes with recommendations for the most effective parameter settings for the best sample elongation (ε) and tensile strength (E).

1. Introduction

Over the last several years, there has been significant growth in demand for materials that are more flexible, durable, and responsive in a range of industries, including engineering and manufacturing, healthcare, and consumer products [1]. Some applications for flexible material and complex design are hard to achieve with traditional methods; recently, additive manufacturing, which is also used as 3D printing, showed high potential to overcome that issue as it is increasingly being used to create end-use parts [2]. Three-dimensional printing, also known as additive manufacturing (AM) technology, involves manufacturing parts directly from 3D digital models. Three-dimensional printing can create complex parts using custom materials and composites with minimal waste [3]. There are several types of 3D printing technologies divided into two categories, which are vat photopolymerization-based printing like stereolithography (SLA) and direct light processing (DLP), and extrusion-based printing like fused deposition modelling (FDM) and direct ink writing (WID) [4,5]. Vat photopolymerization, unlike extrusion, allows high printing resolution due to the low cost; in addition to high resolution, some vat photopolymerization technologies, such as the ones based on liquid crystal display (LCD), are preferred. That variety of techniques makes it applicable to various materials, including shape-memory polymers and stimulus-responsive materials [6]. As vat photopolymerization printing is enhancing and merging with other advanced technologies, it has become a matter of time to use vat photopolymerization with a variety of materials to adapt to the field of the application needed [2,6]. As Duty et al. discussed, not all materials are printable using 3D printing, as there are limitations based on the material’s chemical and physical properties. They found that to properly use a material for 3D printing, it must meet some essential criteria, including the material having the ability to be pressure extruded [7,8]. It should also maintain its shape and form after printing and provide dimensional stability in addition to functionality after printing [1]. Vat photopolymerization is based on having a photosensitive resin material in a tank that gets cured using a light source. With the consideration of all that and knowing the need for more elastic materials that are 3D printable, research was conducted in the area of examining the behavior of elastic materials and the applications of 3D printing with the integration of both to provide high efficiency in the field of additive manufacturing [9]. Several approaches were developed to determine the criteria that must be satisfied by the material and which have the most impact on material selection for 3D printing. Multi-criteria decision analysis (MCDA) is a general term under which many models exist; the main target of MCDA is to evaluate the effect of the criteria on the expected results to determine which is the best solution to be followed for achieving the best results depending on the target and goals in each situation. [10]. This paper discusses the use of LCD printers that provide a highly detailed resolution with minimum material waste in printing elastic material and examines the influence of parameter sets on the final design mechanical properties by using MCDA models.

2. Experimental Setup

2.1. Materials

The selected material for this experiment was acrylated aliphatic urethane-based black resin from the Resione F series (Dongguan Godsaid Technology Co. Ltd., Dongguan, China). The acrylated aliphatic urethane-based resin was selected due to its inherited stretchability and high flexibility. As shown in

Table 1. The mechanical properties of acrylated aliphatic urethane-based resin [11].

Mechanical Property	Acrylated Aliphatic Urethane-Based Resin Data
Shore Hardness	50~60 A
Tear Strength	9.75 KN/m
Tensile Strength	3.8 MPa
Elongation at Break	159%
Viscosity (25 °C)	2300 Mpa·S

, it can be stretched up to 159% though it has relatively high viscosity. Diphenyl (2, 4, 6-trimethyl benzoyl) phosphine oxide (TPO) (MilliporeSigma Canada Ltd., Mississauga, ON, Canada) was used as a photoinitiator.

2.2. Methods

An LCD resin printer (Make: ELEGOO, Model: Mars 3 Pro, https://www.elegoo.com/en-ca (accessed on 14 February 2024), Shenzhen, China) was used for sample printing. An INSTRON 5969 material testing system was utilized for the tensile tests on the samples (ASTM D638-14 standard Type IV [12]). Each sample was printed and tested following the ASTM D638-14 standard. The goal and criteria were selected, and twenty-two (22) samples were printed based on a randomly generated matrix with the variation in the criteria values between the upper and lower limits shown in

Table 2. The goal and criteria of the study.

Goal	Selecting the Optimized 3D Printing Parameters for Higher Stretchability and Strength
Criteria	Upper Limit	Lower Limit
PCT	20 min	10 min
ET	7.5 s	3 s
AC	Under UV protection [UUVP]	In room condition [IRC]
RD	3 axis	1 axis
RT	2 s	1 s
TPO%	3%	0%
AT	3 weeks	1 week

. The selected criteria are post-curing time [PCT], which is the period during which the sample is subjected to UV curing after the printing and washing operations are concluded; exposure time [ET] is the duration for which each layer is exposed to UV during the printing process; aging conditions [AC] describe the conditions in which the sample is held immediately after post-processing until the test is completed; rotation direction [RD] sets the direction and how many rotations are performed before adding the supports in the software to prepare the file for printing; rest time after lift [RT] explains the time the built plate takes from the end of the last layer to the beginning of the next layer during the printing process; photo-initiator effect [TPO%] as the resin used for each sample contains a different percentage of photo-initiator to test its effect on the curing and strength; and aging time [AT] is the time between the end of the post-processing stage and the testing stage. The results of these printings are shown in

Table 3. The tensile test results for the 22 samples.

Samples	1	2	3	4	5	6	7	8	9	10	11	12
E [MPa]	4.25	4.05	4.56	3.95	4.81	4.49	4.59	3.94	4.84	4.08	4.07	4.30
ε [%]	104.29	91.96	65.28	93.24	62.89	60.06	71.70	77.09	70.06	103.10	108.52	78.00
Samples	13	14	15	16	17	18	19	20	21	22
E [MPa]	4.72	4.20	4.07	4.33	4.10	4.27	4.52	3.84	4.30	4.19
ε [%]	57.21	91.45	108.59	73.06	99.75	72.02	64.78	61.00	114.06	60.56

. The steps followed in the MCDA analysis are illustrated in the flow chart shown in Figure 1.

3. Analytic Hierarchy Process (AHP)

Step 1: Define the decision hierarchy by determining the decision problem’s main goal, criteria, and alternatives. They were categorized on three levels, and the hierarchical structure was created as shown in Figure 2 [13,14].

Step 2: Conduct pairwise comparisons for each set of criteria and options to assess their relative value [15].

Step 3: Conduct pairwise comparisons for each set of criteria and options to assess their relative value. The pairwise comparison ranks the criterion in row i (i = 1, 2, 3, …, n) against each of the n columns’ criteria, which results in a square matrix A_ij.

Step 4: Calculate the geometric mean of rows, then obtain the normalized weight (W_j) of each criterion by dividing each row’s geometric mean by the sum of all geometric mean as shown in Equations (1) and (2).

$${{GM}_{\mathit{j}}=\left[{\prod }_{j=1}^N{a}_{ij}\right]}^{{\displaystyle \frac{1}{N}}}$$

(1)

$$W_j={\displaystyle \frac{{GM}_j}{{\sum }_{j=1}^N{GM}_j}}$$

(2)

Step 5: Now perform the consistency check by calculating the consistency index (CI) from Equation (3), then use the value of the random index (RI) given in

Table 4. Shows the random index (RI) values concerning N.

N	2	3	4	5	6	7	8	9	10
RI	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.51

to calculate the consistency ratio (CR) in Equation (4).

$$CI={\displaystyle \frac{({\lambda }_{max}-N)}{(N-1)}}$$

(3)

where N is the number of criteria involved in the analysis, and ${\lambda }_{max}$ is the matrix multiplication of W_j and A_ij.

$$CR={\displaystyle \frac{CI}{RI}}$$

(4)

The W_j matrix is said to be consistent when CR ≤ 0.1, and according to Saaty [13], the matrix is consistent and expert opinion is good to further continue the analysis; otherwise, new data collection is required as shown in Figure 1.

4. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

Step 1: Normalize the decision matrix (x_ij) of n criteria and m alternatives after changing the qualitative values into quantitative values, then use Equation (5) [16,17].

$$n_{ij}={\displaystyle \frac{x_{ij}}{\sqrt{{\sum }_{i=1}^n{x}_{ij}^2}}}$$

(5)

Step 2: Calculate the weighted normalized matrix (D_ij) by multiplying each cell value in the row representing the criteria by the weight of that criteria.

Step 3: Calculate the positive ideal solution (A*) and negative ideal solution (A⁻) as follows:

A* = {(max i d_ij|j $\in$ J), (min i d_ij|j $\in$ J′) for i = 1, 2, 3, …, n}, and A⁻ = {(min i d_ij|j $\in$ J), (max i d_ij|j $\in$ J′ for i = 1, 2, 3, …, n}, where J represents the set of beneficial criteria, and J′ represents the set of cost criteria.

Step 4: Calculate the positive ideal separation distance S* from the positive ideal solution as in Equation (6) and the negative ideal separation distance S⁻ from the negative ideal solution by Equation (7).

$$S_i^{*}=\sqrt{{\sum }_{j=1}^m\left(d_{ij}-d_j^{*}\right)2}$$

(6)

$$S_i^{-}=\sqrt{{\sum }_{j=1}^m\left(d_{ij}-d_j^{-}\right)2}$$

(7)

Step 5: The last step is to calculate the closeness coefficient (${CC}_i^{*}$) to the ideal solutions, like in Equation (8).

$${CC}_i^{*}={\displaystyle \frac{S_i^{-}}{S_i^{*}+S_i^{-}}}$$

(8)

The values of ${CC}_i^{*}$ should be 0 < ${CC}_i^{*}$ < 1, where i = 1, 2, 3, …, n. Then, according to these values, the ranking is conducted for the alternatives in descending order, which means the lower the ${CC}_i^{*}$ value, the better the result.

5. Results and Discussion

By following the steps of AHP and TOPSIS to conduct the analysis, according to the AHP analysis, the pairwise comparison, which is shown in

Table 5. Shows the pairwise comparison used in AHP analysis.

Criteria	PCT	ET	AC	RD	RT	TPO%	AT
PCT	1.00	1.00	2.00	0.33	2.00	3.00	3.00
ET	1.00	1.00	2.00	2.00	3.00	3.00	3.00
AC	0.50	0.50	1.00	0.50	2.00	0.50	2.00
RD	2.00	0.50	2.00	1.00	2.00	2.00	1.00
RT	0.50	0.33	0.50	0.50	1.00	2.00	0.50
TPO%	0.33	0.33	2.00	0.50	0.50	1.00	3.00
AT	0.33	0.33	0.50	1.00	2.00	0.33	1.00

, was used to calculate the weight results shown in

Table 6. Shows the weights of the criteria by AHP, based on collected data from the literature and expert opinions [18].

Criteria	PCT	ET	AC	RD	RT	TPO%	AT
Weights	0.19	0.26	0.11	0.18	0.08	0.10	0.08

. The criterion with the highest effect on the tensile strength and elongation based on the results is expected to be exposure time (ET).

The AHP analysis was performed twice, once for the seven criteria to figure out which criterion is expected to have the highest effect on the results, and another time for the result values E [MPa] and ε [%] with equal weights of 0.5. The weight values of the results were then used in the TOPSIS analysis to conduct the ranking by considering all criteria as beneficial factors, except for TPO% and ET. As for the TPO%, it was found during the sample printing and preparation that the higher the TPO%, the more fragile the sample becomes till it reaches 3%, which represents the upper limit as higher percentages of TPO are not printable. Hence, it was concluded that the TPO% is a cost factor. As for ET, which is the exposure time for each printed layer to UV during printing before the built plate is leveled up, allowing more resin to flow and another layer to be printed, the higher the ET, the better the bonding among molecules in each layer by itself; however, as the layer becomes almost fully cured and the intermolecular bonding is fulfilled, the adhesion with the next layers becomes weak, causing a phenomenon called “layer separation”, in which layers detach from each other. Hence, ET is also considered a cost factor. The ranking was conducted using the results analysis, as the E and ε weights were used to conduct a TOPSIS analysis by combining the weighted normalized value for both results E and ε and then continuing the rest of the analysis to find the ranking of the alternatives. It was found that sample 21 had the best combination of set parameters to give the optimized results with its E = 4.300 MPa, knowing that the maximum tensile strength was E = 4.840 MPa and the maximum percentage elongation found among the twenty-two (22) samples was ε = 114.060%. It was also found that according to the weight calculations performed in the AHP analysis, ET has the highest influence on the quality of the printed part in the case of using acrylated aliphatic urethane-based resin.

6. Conclusions

This paper examines the behavior of acrylated aliphatic urethane-based resin, an elastic 3D-printed resin, according to the ASTM 638-14 Type IV standard, under axial tensile stress. The objective of this research is to explore how changes in parameter sets impact the final properties of the samples, particularly tensile strength and percentage elongation. By adjusting these parameters during and after printing, we aim to improve the quality and strength of the final product. Given the variation in results and the discrepancy between the best sample in terms of E [MPa] and ε [%], additional data analysis was performed using AHP and TOPSIS techniques to establish a relationship between the results and parameter sets, ranking the samples and identifying the optimal parameter set with optimized outcomes. These optimized parameters can facilitate the development of robust designs that remain elastic, crucial for applications requiring both features and susceptibility to aging-induced deformation, such as building materials. The novelty of this research and the scarcity of literature in this domain suggest opportunities for further exploration, not only in material selection but also in understanding material behavior during 3D printing with varied parameter settings. The application of MCDA models has proven to be a valuable tool for assessing and prioritizing mechanical properties, setting the stage for future advancements in materials science and engineering.