# Analysis and Design of Lattice Structures for Rapid-Investment Casting

^{*}

## Abstract

**:**

## 1. Introduction

- A methodology to study the RIC performance of lattice structures is presented to test our hypothesis on the lattice topological features.
- The features are compared and analyzed with the test results, and a set of design guidelines for RIC is created.
- Based on the analysis, new lattice structures are designed and tested for RIC performance.

#### Literature Review

## 2. Materials and Methods

#### 2.1. Materials and Equipment

^{®}, Albuquerque, NM, USA), see Figure 1b. A high strength plaster—the Ransom and Randolph Ultra-Vest Maxx—is used as the mold material. The plaster is prepared with the St. Louis 92-4 KG digital vacuum investment mixer (CIMO, Vigevano, PV, Italy), see Figure 1c. Heating of the mold is done in the L17-K12 Furnace (Lucifer, Warrington, PA, USA), see Figure 1d. The casting machine used is the J-2R™ (Neutec

^{®}, Albuquerque, NM, USA), see Figure 1e. Two casting materials are used in the experiments. One is recycled 70-30 brass with a density of $8.73\times {10}^{3}$ g/mm${}^{3}$, and the other is recycled 6061 aluminum with a density of $2.7\times {10}^{3}$ g/mm${}^{3}$. Brass is known of with fine details and used for detailed miniatures, sculptures, and jewelry; aluminum is commonly used for lightweight aerospace and automotive applications such as heat exchangers. Since the objective of this paper is to find out the effect of lattice topology on casting performance, these two materials being used is to show that the findings are consistent in materials with quite different properties. The DenPlus Basic Eco Sandblaster is used for post-processing (Figure 1f), and the glass beads used for sandblasting have a size of 50 microns.

#### 2.2. Manufacturing Process

#### 2.2.1. Pattern Making

#### 2.2.2. Mold Making and Burnout

#### 2.2.3. Casting

#### 2.2.4. Quenching and Post-Processing

#### 2.3. Lattice Designs

#### 2.3.1. Set 1

#### 2.3.2. Set 2

#### 2.4. Characterization

#### 2.4.1. Mold Flow Simulation

#### 2.4.2. Mechanical Finite Element Analysis

#### 2.4.3. Microscopic Analysis

## 3. Results

#### 3.1. Mold Flow

#### 3.2. Cast 1

#### 3.3. Cast 2

#### 3.4. Mechanical Properties

#### 3.5. Voids and Grain Structures

## 4. Discussion

#### Design Guidelines

- The relative strut size should be kept below 0.2.
- The number of joints should be kept below 9.
- The max and mean joint valence of 8 or less is recommended.
- For mechanical performance, the strut angle distribution should include vertical, diagonal, and horizontal struts.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Dong, G.; Tang, Y.; Li, D.; Zhao, Y.F. Design and optimization of solid lattice hybrid structures fabricated by additive manufacturing. Addit. Manuf.
**2020**, 33, 101116. [Google Scholar] [CrossRef] - Yan, L.; Zhao, L.P.; O’Neill, G.K. Dimensional consistency of SLM printed orthopaedic implants designed using lightweight structures. Trans. Addit. Manuf. Meets Med.
**2020**, 2. [Google Scholar] [CrossRef] - Harun, W.; Kamariah, M.; Muhamad, N.; Ghani, S.; Ahmad, F.; Mohamed, Z. A review of powder additive manufacturing processes for metallic biomaterials. Powder Technol.
**2018**, 327, 128–151. [Google Scholar] [CrossRef] - Aboulkhair, N.T.; Simonelli, M.; Parry, L.; Ashcroft, I.; Tuck, C.; Hague, R. 3D printing of Aluminium alloys: Additive Manufacturing of Aluminium alloys using selective laser melting. Prog. Mater. Sci.
**2019**, 106, 100578. [Google Scholar] [CrossRef] - Maconachie, T.; Leary, M.; Lozanovski, B.; Zhang, X.; Qian, M.; Faruque, O.; Brandt, M. SLM lattice structures: Properties, performance, applications and challenges. Mater. Des.
**2019**, 183, 108137. [Google Scholar] [CrossRef] - Carneiro, V.H.; Rawson, S.D.; Puga, H.; Meireles, J.; Withers, P.J. Additive manufacturing assisted investment casting: A low-cost method to fabricate periodic metallic cellular lattices. Addit. Manuf.
**2020**, 33, 101085. [Google Scholar] [CrossRef] - Huang, Y.; Xue, Y.; Wang, X.; Han, F. Effect of cross sectional shape of struts on the mechanical properties of aluminum based pyramidal lattice structures. Mater. Lett.
**2017**, 202, 55–58. [Google Scholar] [CrossRef] - Puga, H.; Carneiro, V.H.; Correira, P.; Vieira, V.; Barbosa, J.; Meireles, J. Mechanical behavior of honeycomb lattices manufactured by investment casting for scaffolding applications. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl.
**2017**, 231, 73–81. [Google Scholar] [CrossRef] - Khirsariya, N.A.; Kagthara, M.S.; Mandalia, P.H. Reduction of Shrinkage Defect in Valve Body Casting Using Simulation Software. Int. J. Eng. Sci. Res. Technol.
**2014**, 3, 5021–5024. [Google Scholar] - Kuo, J.K.; Huang, P.H.; Lai, H.Y.; Chen, J.R. Optimal gating system design for investment casting of 17-4PH stainless steel enclosed impeller by numerical simulation and experimental verification. Int. J. Adv. Manuf. Technol.
**2017**, 92, 1093–1103. [Google Scholar] [CrossRef] - Wang, D.; Sun, J.; Dong, A.; Shu, D.; Zhu, G.; Sun, B. An optimization method of gating system for impeller by RSM and simulation in investment casting. Int. J. Adv. Manuf. Technol.
**2018**, 98, 3105–3114. [Google Scholar] [CrossRef] - Li, F.; Wang, Y.; Wang, D.; Zhao, Y.; Qi, C.; Sun, B. Comparison of various gating systems for investment casting of hydraulic retarder impeller with complex geometry. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.
**2021**, 235, 583–593. [Google Scholar] [CrossRef] - Bruna, M.; Bolibruchová, D.; Pastirčák, R.; Remišová, A. Gating System Design Optimization for Investment Casting Process. J. Mater. Eng. Perform.
**2019**, 28, 3887–3893. [Google Scholar] [CrossRef] - Sama, S.R.; Badamo, T.; Lynch, P.; Manogharan, G. Novel sprue designs in metal casting via 3D sand-printing. Addit. Manuf.
**2019**, 25, 563–578. [Google Scholar] [CrossRef] - Maidin, S.; Yi, T.; Hambali, A.; Akmal, S.; Hambali, R.; Abdullah, Z. Investigation of optimum gating system design of fused deposition modelling pattern for sand casting. J. Mechan. Eng. Sci.
**2017**, 11, 2801–2814. [Google Scholar] [CrossRef] - Yu, J.; Wang, D.; Li, D.; Tang, D.; Hao, X.; Tan, S.; Shu, D.; Peng, Y.; Sun, B. Engineering computing and data-driven for gating system design in investment casting. Int. J. Adv. Manuf. Technol.
**2020**, 111, 829–837. [Google Scholar] [CrossRef] - Richard, C.T.; Kwok, T.-H. Rapid Investment Casting: Design and Manufacturing Technologies. In Proceedings of the 39th Computers and Information in Engineering Conference, Anaheim, CA, USA, 18–21 August 2019. [Google Scholar] [CrossRef]
- Wang, J.; Sama, S.R.; Lynch, P.C.; Manogharan, G. Design and topology optimization of 3D-Printed wax patterns for rapid investment casting. Procedia Manuf.
**2019**, 34, 683–694. [Google Scholar] [CrossRef] - Singh, J.; Singh, R.; Singh, H. Dimensional accuracy and surface finish of biomedical implant fabricated as rapid investment casting for small to medium quantity production. J. Manuf. Process.
**2017**, 25, 201–211. [Google Scholar] [CrossRef] - Marwah, O.; Sharif, S.; Ibrahim, M.; Mohamad, E.; Idris, M. Direct rapid prototyping evaluation on multijet and fused deposition modeling patterns for investment casting. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl.
**2016**, 230, 949–958. [Google Scholar] [CrossRef] - Ishida, Y.; Miyasaka, T. Dimensional accuracy of dental casting patterns created by 3D printers. Dent. Mater. J.
**2016**, 35, 250–256. [Google Scholar] [CrossRef][Green Version] - Mukhtarkhanov, M.; Perveen, A.; Talamona, D. Application of Stereolithography Based 3D Printing Technology in Investment Casting. Micromachines
**2020**, 11, 946. [Google Scholar] [CrossRef] - Al-Ketan, O.; Rowshan, R.; Al-Rub, R.K.A. Topology-mechanical property relationship of 3D printed strut, skeletal, and sheet based periodic metallic cellular materials. Addit. Manuf.
**2018**, 19, 167–183. [Google Scholar] [CrossRef] - Wang, H.; Fu, Y.; Su, M.; Hao, H. A novel method of indirect rapid prototyping to fabricate the ordered porous aluminum with controllable dimension variation and their properties. J. Mater. Process. Technol.
**2019**, 266, 373–380. [Google Scholar] [CrossRef] - Li, D.; Liao, W.; Dai, N.; Dong, G.; Tang, Y.; Xie, Y.M. Optimal design and modeling of gyroid-based functionally graded cellular structures for additive manufacturing. Comput. Aided Des.
**2018**, 104, 87–99. [Google Scholar] [CrossRef] - Wagner, M.A.; Lumpe, T.S.; Chen, T.; Shea, K. Programmable, active lattice structures: Unifying stretch-dominated and bending-dominated topologies. Extrem. Mech. Lett.
**2019**, 29, 100461. [Google Scholar] [CrossRef] - Alabort, E.; Barba, D.; Reed, R.C. Design of metallic bone by additive manufacturing. Scr. Mater.
**2019**, 164, 110–114. [Google Scholar] [CrossRef] - Matte, C.D.; Pearson, M.; Trottier-Cournoyer, F.; Dafoe, A.; Kwok, T.H. Automated storage and active cleaning for multi-material digital-light-processing printer. Rapid Prototyp. J.
**2019**, 25, 864–874. [Google Scholar] [CrossRef] - Després, N.; Cyr, E.; Mohammadi, M. A performance metric for additively manufactured microlattice structures under different loading conditions. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl.
**2019**, 233, 1814–1829. [Google Scholar] [CrossRef] - Li, C.; Lei, H.; Zhang, Z.; Zhang, X.; Zhou, H.; Wang, P.; Fang, D. Architecture design of periodic truss-lattice cells for additive manufacturing. Addit. Manuf.
**2020**, 34, 101172. [Google Scholar] [CrossRef] - Chen, W.; Watts, S.; Jackson, J.A.; Smith, W.L.; Tortorelli, D.A.; Spadaccini, C.M. Stiff isotropic lattices beyond the Maxwell criterion. Sci. Adv.
**2019**, 5, eaaw1937. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**RIC process: (

**a**) DLP AM. (

**b**) Pattern spruing. (

**c**) Plaster mold making. (

**d**) Pattern burnout. (

**e**) Vacuum casting. (

**f**) Post-processing.

**Figure 3.**Test 1 lattice cells and structure: (

**a**) Rhombic. (

**b**) Kelvin Cell. (

**c**) Cubic. (

**d**) Octet-Truss. (

**e**) $2\times 2\times 6$ structure.

**Figure 4.**Test 2 lattice cells and structure: (

**a**) Proposed cell. (

**b**) Hourglass. (

**c**) Rhombic. (

**d**) Octet-Truss. (

**e**) $5\times 5\times 5$ structure.

**Figure 5.**Tensile loading conditions: (

**a**) Displacement allowed only in Z. (

**b**) Applied force. (

**c**) Fixed support. Shear loading conditions: (

**d**) Applied force. (

**e**) Fixed support. (

**f**,

**g**) Displacement allowed only in X and Y.

**Figure 9.**Set 2 printed patterns: (

**a**) Proposed cell, (

**b**) Hourglass, (

**c**) Rhombic, and (

**d**) Octet-Truss.

**Figure 10.**Set 2 cast structures: (

**a**) Proposed cell, (

**b**) Hourglass, (

**c**) Rhombic, and (

**d**) Octet-Truss.

**Figure 13.**Microscopic analysis for porosity using optical microscopy. Images $50\times $ magnification.

Property | Value | Unit |
---|---|---|

Material | CW505L Brass | N/A |

Molding Material | Plaster | N/A |

Melting Temp. | 1093 | °C |

Preheat Temp. | 538 | °C |

Shell Mold Thickness | 50 | mm |

Property | Value | Unit |
---|---|---|

Density | 8530 | kg/m^{3} |

Young’s Modulus | $10\times {10}^{10}$ | Pa |

Poisson’s Ratio | $0.331$ | |

Bulk Modulus | $8.08678\times {10}^{10}$ | Pa |

Shear Modulus | $3.080390\times {10}^{10}$ | Pa |

Rhombic | Kelvin Cell | |||||

Mass (g) | Cell Width (mm) | Strut Diameter (mm) | Mass (g) | Cell Width (mm) | Strut Diameter (mm) | |

CAD | 47.162 | 20.00 | 1.980 | 47.163 | 20.00 | 1.976 |

Printed | N/A | 20.23 | 2.013 | N/A | 20.21 | 2.090 |

Cast | 49.000 | 20.19 | 2.077 | 45.840 | 20.15 | 2.047 |

% Fill | 103.90 | 97.19 | ||||

Cubic | Octet-Truss | |||||

Mass (g) | Cell Width (mm) | Strut Diameter (mm) | Mass (g) | Cell Width (mm) | Strut Diameter (mm) | |

CAD | 47.142 | 20.00 | 1.629 | 47.163 | 20.00 | 1.373 |

Printed | N/A | 20.20 | 1.723 | N/A | 20.08 | 1.447 |

Cast | 40.350 | 20.15 | 1.693 | 38.500 | 20.11 | 1.417 |

% Fill | 85.59 | 81.63 |

Hourglass | Proposed Cell | |||||

Mass (g) | Cell Width (mm) | Strut Diameter (mm) | Mass (g) | Cell Width (mm) | Strut Diameter (mm) | |

CAD | 12.005 | 25.00 | 1.022 | 12.004 | 25.00 | 1.111 |

Printed | N/A | 25.19 | 1.013 | N/A | 25.02 | 1.147 |

Cast | 13.030 | 25.01 | 1.157 | 12.750 | 24.93 | 1.113 |

% Fill | 108.54 | 106.21 | ||||

Rhombic | Octet-Truss | |||||

Mass (g) | Cell Width (mm) | Strut Diameter (mm) | Mass (g) | Cell Width (mm) | Strut Diameter (mm) | |

CAD | 12.005 | 25.00 | 0.989 | 12.005 | 25.00 | 0.686 |

Printed | N/A | 25.18 | 1.028 | N/A | 25.10 | 0.743 |

Cast | 12.540 | 24.86 | 1.003 | 11.740 | 20.08 | 1.447 |

% Fill | 104.46 | 97.79 |

**Table 5.**Geometric stiffness for simulated Ansys lattice structures. ${\mathbf{E}}_{\mathbf{eq}}$ is the Equivalent Tensile Modulus and ${\mathbf{G}}_{\mathbf{eq}}$ is the Equivalent Shear Modulus.

Topology | ${\mathbf{E}}_{\mathbf{eq}}$ (Mpa) | ${\mathbf{G}}_{\mathbf{eq}}$ (Mpa) |
---|---|---|

Rhombic | 14,528 | 3387.3 |

Kelvin | 12,849 | 2005.9 |

Cubic | 24,941 | 1214.8 |

Octet-Truss | 11,710 | 3478.2 |

Proposed Cell | 23,501 | 3978.4 |

Hourglass | 24,847 | 36,225.0 |

2-Valence | 4-Valence | 6-Valence | |
---|---|---|---|

Sum of void area | 28,946 | 199,025 | 786,608 |

Max void area | 1555 | 129,721 | 82,656 |

Min void area | 20 | 20 | 20 |

Total void # | 154 | 326 | 1209 |

Total strut area | 13,579,304 | 13,729,209 | 23,476,110 |

Void ratio (%) | 0.21 | 1.45 | 3.35 |

Proposed | Hourglass | Rhombic | Cubic | Kelvin Cell | Octet-Truss | |
---|---|---|---|---|---|---|

Relative Strut Size | 0.22 | 0.20 | 0.20 | 0.16 | 0.20 | 0.14 |

Number of Joints | 9 | 9 | 9 | 27 | 24 | 14 |

Max Joint Valence | 6 | 6 | 8 | 6 | 4 | 16 |

Min Joint Valence | 4 | 4 | 8 | 6 | 4 | 16 |

Mean Joint Valence | 4.58 | 5.74 | 8 | 6 | 4 | 16 |

Proposed | Hourglass | Rhombic | Kelvin | Cubic | Octet-Truss | |
---|---|---|---|---|---|---|

Relative Strut Size | 4 | 4 | 3 | 3 | 2 | 1 |

Number of Joints | 4 | 4 | 4 | 1 | 1 | 2 |

Joint Valence | 3 | 3 | 3 | 4 | 3 | 1 |

Strut Angle Distribution | 4 | 3 | 3 | 3 | 2 | 3 |

Tensile | 4 | 4 | 3 | 3 | 4 | 2 |

Shear | 4 | 4 | 4 | 2 | 1 | 4 |

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**MDPI and ACS Style**

Richard, C.T.; Kwok, T.-H. Analysis and Design of Lattice Structures for Rapid-Investment Casting. *Materials* **2021**, *14*, 4867.
https://doi.org/10.3390/ma14174867

**AMA Style**

Richard CT, Kwok T-H. Analysis and Design of Lattice Structures for Rapid-Investment Casting. *Materials*. 2021; 14(17):4867.
https://doi.org/10.3390/ma14174867

**Chicago/Turabian Style**

Richard, Christopher T., and Tsz-Ho Kwok. 2021. "Analysis and Design of Lattice Structures for Rapid-Investment Casting" *Materials* 14, no. 17: 4867.
https://doi.org/10.3390/ma14174867