# Flexible Investment Casting Wax Patterns for 3D-Printing: Their Rheological and Mechanical Characterizations

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental

#### 2.1. Chemicals

#### 2.2. Sample Preparation

#### 2.3. Instrumental Methods

^{−1}to 150 s

^{−1}using a ramp time of 2.5 min. For viscosity versus temperature measurements in the temperature range of 60 °C–120 °C, a shear rate of 10 s

^{−1}and temperature ramp of 2 °C/min were employed. We used the shear rate of 10 s

^{−1}based on a recommendation from T. Mezger, which is a local laboratory standard for the investigation of such kinds of waxes [18].

_{f}is the flexural stress; F is the applied force in Newton; and L, b and h are the span in millimeters, the width in millimeters of the specimen and the thickness in millimeters, respectively.

_{f}, s, h and L are the flexural strain parameter (dimensionless), the deflection in millimeters, the thickness of the specimen in millimeters and the span in millimeters, respectively.

_{f}, σ

_{f2}and σ

_{f1}are the flexural modulus in MPa, the flexural stress at ε

_{f2}in MPa, and the flexural stress at ε

_{f1}in MPa, respectively, and ε

_{f2}= 0.0025 and ε

_{f1}= 0.0005.

## 3. Results and Discussion

#### 3.1. Rheological Properties

_{6}to C

_{18}) greatly reduced the pour point of the crude oil, thereby preventing the precipitation of the wax [20]. In our case, however, no such effect was observed, probably due to the lack of long carbon chains and hydroxyl groups. Thus, the absence of considerable pour point depression is advantageous in our case, since the blends retain their pour points close to that of the pure hydrocarbon wax, independent from the compositions.

_{η}/R, E

_{η}and R are the activation energy and the universal gas constant, respectively.

_{w,Escorene}curves can adequately be described at all temperatures by a stretched exponential model, as shown in Equation (5).

_{w,Escorene}relationships with a wide range of X

_{w,Escorene}values. Interestingly, in other chemical systems, single exponential relationships were found between the viscosity and composition, such as in the case of the dimer–trimers of hexamethylene–diisocyanate [22] and the terner system of propylene glycol, glycerol and water [23].

^{−1}–160 s

^{−1}. A similar trend can be observed for the rest of the samples as well. Furthermore, it was found that with the increasing Piccotex content, i.e., with the decreasing Escorene content, the shear stress versus shear rate curves became linear, even at temperatures close to the pour point in the case of blends with low Escorene contents. On the contrary, at temperatures close to the pour point for blends with high Escorene contents, the shear stress–shear rate curves obey the Ostwald–de Waele equation (Equation (6)) with a power of n < 1 (non–Newtonian, shear thinning fluid with pseudoplasticity). The shear stress–shear rate curves for samples #01–#16 recorded at 90 °C and the viscosity versus shear rate curves for sample #07 in the temperature range of 75 °C–110 °C are presented in Figures S3–S14 in the Supporting Information, respectively.

_{1}is a constant, a measure of the consistency of the fluid.

^{−1}(Figure S15). Furthermore, in line with this observation, in the case of the samples that showed no maximum as a function of the shear rates, the mixture remained clear over the entire shear rate range investigated. In addition, it turned out that when decreasing the Escorene content, the blends tended to behave as a Newtonian fluid. For example, in the case of sample #16, only a small deviation from the Newtonian property can be observed at 75 °C, i.e., near the pour point (Figure S8). Note that sample #01 contains Escorene, while sample #16 only contains Piccotex in addition to the DMW7478 wax. Thus, it can be concluded from this finding that the interaction leading to crystallization or co-crystallization takes place primarily between the DMW7478 wax and the Escorene, which is, as mentioned before, an ethylene–vinyl acetate (EVA) copolymer. Interestingly, the interaction of wax in crude oil with an EVA copolymer is believed to be the main reason for the depressant effect on the pour point of the EVA copolymers [27,28].

_{c}

_{d}and k

_{c}are the rate constants for the dissolution and formation of the crystalline phase, and m is the power of the shear rate.

_{c}), the molecules start to organize themselves into crystals, whereas if (dγ/dt)

_{c}is lower, then no crystallization takes place.

_{1}and c

_{2}as well as n and p are the parameters to be fitted to the experimental data.

_{1}and m parameters of Equation (9) can be determined using the range of the shear rate up to the maximum shear stress, since in this region, it is supposed that no considerable amount of crystals was formed, allowing us to estimate the values of c

_{1}and m. As it can be recognized in Figure 5, very good fittings to the experimental data were obtained. It is to be noted, however, that in order to validate the model, additional independent experiments need to be performed, e.g., to establish the cross-correlation between the parameters of the proposed model (if any) (Equations (7)–(9)).

#### 3.2. Mechanical Properties

_{w,Piccotex}= 0.45; however, at higher X

_{w,Piccotex}values, a considerable increase in the values of the Young’s modulus can be attained, as demonstrated in Figure 7.

_{1}, d

_{2}, d

_{3}and d

_{4}are the parameters of the sigmoid function characterizing a hypothetical distribution.

_{1}= E, b

_{2}= (dε/dt)η

_{1}/E, b

_{3}= E

_{1}/(dε/dt)/η

_{1}, b

_{4}= (dε/dt)η

_{2}/E, and b

_{5}= E

_{2}/(dε/dt)/η

_{2}; E, E

_{1}and E

_{2}are the Young’s modulus of the corresponding branches; and η

_{1}and η

_{2}are the viscosities of the “fluids” in dashpots 1 and 2.

#### 3.3. 3D Printing Application of the Blends

## 4. Conclusions

## Supplementary Materials

^{−1}(a) and 100 s

^{−1}(b) at temperature of 85 °C; Figure S16: The measured and the fitted σ versus ε data for the sample #01; Figure S17: The measured and the fitted σ versus ε data for the sample #03; Figure S18: The measured and the fitted σ versus ε data for the sample #04; Figure S19: The measured and the fitted σ versus ε data for the sample #05; Figure S20: The measured and the fitted σ versus ε data for the sample #06; Figure S21: The measured and the fitted σ versus ε data for the sample #08; Figure S22: The measured and the fitted σ versus ε data for the sample #10; Figure S23: The measured and the fitted σ versus ε data for the sample #11; Figure S24: The measured and the fitted σ versus ε data for the sample #12; Figure S25: The measured and the fitted σ versus ε data for the sample #13; Figure S26: The measured and the fitted σ versus ε data for the sample #14; Figure S27: The measured and the fitted σ versus ε data for the sample #15; Figure S28: The measured and the fitted σ versus ε data for the sample #16; Table S1: The values of A and B of the Arrhenius-Guzman equation determined by fitting.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Variation in the dynamic viscosities with temperature and compositions for pure microcrystalline wax DMW7478 and sample #08. The shear rate was 10 s

^{−1}. The arrows show the corresponding axis.

**Figure 2.**Variation in the dη/dT values at the pour point with the Piccotex content. The shear rate was 10 s

^{−1}.

**Figure 3.**The dependence of the viscosity on the temperature in the range of 75 °C –120 °C for samples #02, #07 and #09. The solid and the dashed lines stand for the measured and fitted (via Equation (4)) curves. The shear rate was 10 s

^{−1}. The fitted parameters are A = 1.65 × 10

^{−5}, 1.40 × 10

^{−6}and 4.10 × 10

^{−7}Pas, and B = 5498, 5865 and 6062 K for samples #02, #07 and #09, respectively.

**Figure 4.**The viscosity versus weight fraction of Escorene at temperatures of 90 °C, 105 °C and 120 °C. The inset shows the ln(η) versus X

_{w,Escorene}curves. The symbols and the dashed lines stand for the experimental and the fitted data (via Equation (5)), respectively. The fitted parameters are: α = 0.045, 0.089, 0.230; β = 28.5, 24.3, 19.3; and γ = 0.616, 0.640, 0.673. The shear rate was 10 s

^{−1}.

**Figure 5.**Shear stress versus shear rate curves for sample #07 at 75 °C, 80 °C, 85 °C and 90 °C. The symbols and solid lines represent the experimental and the fitted curves via Equations (7)–(9). The fitted parameters are as follows: 75 °C: a = 3.36 × 10

^{−4}, b = 3.95 × 10

^{−4}, m = 0.54, c

_{1}= 276.1, n = 0.52, c

_{2}= 126.2 and p = 0.40; 80 °C: a = 2.43 × 10

^{−3}, b = 2.35 × 10

^{−4}, m = 0.61, c

_{1}= 21.8, n = 1.0, c

_{2}= 9.7 and p = 0.18; 85 °C: a = 3.10 × 10

^{−3}, b = 4.32 × 10

^{−5}, m = 1.15, c

_{1}= 17.5, n = 1.0, c

_{2}= 2.0 and p = 1.0; 90 °C: c

_{1}= 17.5, n = 1.0, c

_{2}= 2.0; and all the other parameters are 0.

**Figure 7.**Variation in the Young’s modulus with the weight fraction of Piccotex. The dashed curve is the fitted curve via Equation (10). The fitted parameters are as follows: d

_{1}= 51.8 MPa, d

_{2}= 65.7 MPa, d

_{3}= 60.1 and d

_{4}= 4.6.

**Figure 8.**Viscoelastic standard linear solid (SLS) model extended with an additional Maxwell element (a spring and a dashpot in the series).

**Figure 9.**The measured (solid curves) and the fitted (dashed curves) σ versus ε data for samples #02, #07 and #09. The fitted parameters are as follows: b

_{1}= 0.07 MPa, b

_{2}= 14.03, b

_{3}= 41.94, b

_{4}= 2.31, b

_{5}= 8.61 for sample #02; b

_{1}= 0.02 MPa, b

_{2}= 53.57, b

_{3}= 29.16, b

_{4}= 0.90, b

_{5}= 7.52 for sample #07; and b

_{1}= 0.05MPa, b

_{2}= 18.20, b

_{3}= 48.21, b

_{4}= 1.00, b

_{5}= 12.30 for sample #09. Please note that the pairs of values of (b

_{2},b

_{3}) and (b

_{4},b

_{5}) are interchangeable.

**Figure 10.**The ratings of blend samples #01–#16 according to their spooling suitability and printability.

**Figure 11.**Ratings of the blends in terms of their capability for 3D printing. The scores given are detailed in Figure 10.

**Figure 12.**3D-printed objects printed from wax pattern #08: (

**a**) Cat (small toy), (

**b**) mixer and (

**c**) boat propeller.

**Table 1.**The compositions of the wax samples made of microcrystalline wax (DMW7478), Piccotex 75 and Escorene.

Sample | DMW7478 % (m/m) | Piccotex 75 % (m/m) | Escorene % (m/m) |
---|---|---|---|

#01 | 28 | 0 | 72 |

#02 | 28 | 5 | 67 |

#03 | 28 | 10 | 62 |

#04 | 28 | 15 | 57 |

#05 | 28 | 20 | 52 |

#06 | 28 | 25 | 47 |

#07 | 28 | 30 | 42 |

#08 | 28 | 35 | 37 |

#09 | 28 | 40 | 32 |

#10 | 28 | 45 | 27 |

#11 | 28 | 50 | 22 |

#12 | 28 | 55 | 17 |

#13 | 28 | 60 | 12 |

#14 | 28 | 65 | 7 |

#15 | 28 | 70 | 2 |

#16 | 28 | 72 | 0 |

Sample | #01 | #02 | #03 | #04 | #05 | #06 | #07 | #08 |

Pour point (°C) | 72.8 | – | – | 72.2 | 71.9 | 72.0 | 71.5 | 70.6 |

Sample | #09 | #10 | #11 | #12 | #13 | #14 | #15 | #16 |

Pour point (°C) | 71.3 | 71.2 | 70.8 | 70.6 | 69.5 | 70.7 | 71.1 | 72.0 |

**Table 3.**The Young’s modulus, yield stress, yield strain, stress at break, strain at break and flexural modulus for the wax samples.

Sample | Young’s Modulus (MPa) | Yield Stress (MPa) | Yield Strain % | Stress at Break (MPa) | Strain at Break (%) | Flexural Modulus (MPa) |
---|---|---|---|---|---|---|

#01 | 58.24 ± 6.99 | 3.51 ± 0.11 | 27.5 ± 2.1 | 3.08 ± 0.16 | 29.9 ± 2.4 | 62.50 ± 1.46 |

#02 | 52.63 ± 2.18 | 3.12 ± 0.06 | 29.2 ± 1.8 | 2.80 ± 0.08 | 32.7 ± 2.0 | 57.10 ± 1.51 |

#03 | 52.57 ± 3.54 | 3.06 ± 0.06 | 28.9 ± 0.8 | 2.76 ± 0.07 | 31.7 ± 1.4 | 50.00 ± 1.93 |

#04 | 45.01 ± 5.10 | 2.75 ± 0.04 | 29.4 ± 1.6 | 2.43 ± 0.12 | 34.6 ± 0.9 | 54.10 ± 2.31 |

#05 | 45.40 ± 4.91 | 1.35 ± 0.42 | 6.3 ± 3.2 | 0.95 ± 0.51 | 9.6 ± 3.2 | 51.52 ± 1.76 |

#06 | 51.60 ± 4.22 | 2.42 ± 0.07 | 24.3 ± 1.3 | 1.75 ± 0.38 | 26.3 ± 1.6 | 45.81 ± 3.39 |

#07 | 48.41 ± 6.74 | 2.16 ± 0.02 | 28.0 ± 0.8 | 1.68 ± 0.22 | 37.6 ± 1.4 | 50.63 ± 2.98 |

#08 | 60.30 ± 3.44 | 2.16 ± 0.04 | 22.5 ± 0.5 | 1.17 ± 0.05 | 27.6 ± 2.1 | 51.53 ± 0.59 |

#09 | 55.09 ± 4.67 | 1.83 ± 0.07 | 21.1 ± 1.8 | 1.09 ± 0.07 | 30.7 ± 3.6 | 55.06 ± 3.73 |

#10 | 49.90 ± 4.47 | 1.63 ± 0.01 | 18.8 ± 1.3 | 1.10 ± 0.05 | 37.8 ± 1.0 | 58.35 ± 2.52 |

#11 | 64.16 ± 4.36 | 1.61 ± 0.01 | 18.0 ± 0.8 | 1.06 ± 0.03 | 36.9 ± 1.8 | 55.91 ± 3.69 |

#12 | 64.10 ± 7.32 | 1.57 ± 0.06 | 12.8 ± 1.7 | 1.00 ± 0.10 | 21.3 ± 5.2 | 70.95 ± 6.57 |

#13 | 85.67 ± 11.50 | 1.58 ± 0.05 | 10.9 ± 0.25 | 0.98 ± 0.07 | 25.6 ± 6.5 | 70.34 ± 3.12 |

#14 | 99.50 ± 17.68 | 1.78 ± 0.03 | 11.9 ± 0.6 | 1.05 ± 0.05 | 40.6 ± 7.3 | 74.62 ± 4.65 |

#15 | 116.22 ± 21.46 | 1.37 ± 0.14 | 5.9 ± 0.6 | 1.18 ± 0.27 | 11.5 ± 3.6 | 128.29 ± 7.94 |

#16 | 108.50 ± 12.10 | 1.11 ± 0.05 | 6.3 ± 0.3 | 0.37 ± 0.06 | 31.4 ± 8.5 | 200.48 ± 27.63 |

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**MDPI and ACS Style**

Szabó, L.; Deák, G.; Nyul, D.; Kéki, S.
Flexible Investment Casting Wax Patterns for 3D-Printing: Their Rheological and Mechanical Characterizations. *Polymers* **2022**, *14*, 4744.
https://doi.org/10.3390/polym14214744

**AMA Style**

Szabó L, Deák G, Nyul D, Kéki S.
Flexible Investment Casting Wax Patterns for 3D-Printing: Their Rheological and Mechanical Characterizations. *Polymers*. 2022; 14(21):4744.
https://doi.org/10.3390/polym14214744

**Chicago/Turabian Style**

Szabó, László, György Deák, Dávid Nyul, and Sándor Kéki.
2022. "Flexible Investment Casting Wax Patterns for 3D-Printing: Their Rheological and Mechanical Characterizations" *Polymers* 14, no. 21: 4744.
https://doi.org/10.3390/polym14214744