Dynamic Loading of Lattice Structure Made by Selective Laser Melting-Numerical Model with Substitution of Geometrical Imperfections
Abstract
:1. Introduction
2. Materials and Methods
2.1. Speciments Fabrication Using SLM
2.2. Metal Powder Analysis
2.3. Specimens for Mechanical Testing
2.3.1. Tensile Specimens
2.3.2. Lattice Structure Specimens
2.4. Shape of the Struts Analysis
2.5. Mechanical Testing
2.5.1. Quasi-Static Mechanical Testing
2.5.2. Low-Velocity Impact Test
2.6. FEM Numerical Model
3. Results
3.1. The Analysis of Initial Weight and Height
3.2. Optical Measurement of the Lattice Structure
3.3. Mechanical Properties
3.3.1. Quasi-Static Mechanical Testing
3.3.2. Low-Velocity Impact Test Results
3.4. Finite Element Analysis (FEA)
3.4.1. FEA Material Models
3.4.2. FEM Model
4. Discussion
4.1. Substitution of the Strut’s Real Cross-Section with the Ideal Cross-Section
4.2. Application of Numerical Model to BCC Lattice Structures with Struts Diameter between 0.6–1.2 mm
4.3. Mechanical Testing
4.4. Criterion of Damage
5. Conclusions
- The numerical model of BCC micro-lattice structure under dynamic loading with the elliptic strut shape was developed. The results show that the elliptic shape of the lattice structure significantly decreases a deviation between FEA and the measured results compared to the circular cross-section (10%, measured in the first force peak).
- To find the correct mechanical properties for FEA material model, it is necessary to use the struts specimens with appropriate orientation during production due to the influence of internal porosity and surface roughness.
- The orientation during SLM production significantly influences the mechanical properties.
- The shape of the BCC lattice structure was analyzed using optical methods. A distinct “water drop” shape was found in the case of AlSi10Mg alloy.
- A weight comparison of the CAD design and the produced lattice structure shows that for simplification of the “water drop” shape of the strut, the Gaussian strut diameter should be used.
- The results of quasi-static mechanical testing show that the differences between mechanical properties of the 90° and 45° orientation are mainly in the plastic area of deformation and may by caused by the significant surface roughness.
Author Contributions
Funding
Conflicts of Interest
References
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Shortcut | Description | Shortcut | Description |
---|---|---|---|
SLM | Selective laser melting technology | din | Maximum inscribed cylinder into the strut |
FEA | Finite element analysis | dout | Minimum circumscribed cylinder on the strut surface |
FEM | Finite element method | Ar | Cross-section area of real strut |
YLR | Ytterbium fiber laser | ADin | Cross-section area of maximum inscribed cylinder into a strut |
BCC | Body centered cubic | ADgauss | Cross-section area of Gauss strut cylinder |
NM | Numerical model | ADout | Cross-section area of minimum circumscribed cylinder fitted on a strut surface |
STF | Shell thickness factor | Aellipse | Cross-section area of an ellipse fitted to the strut surface |
CAD | Computer aided design | a | Ellipse minor axes |
EPS | Equivalent Plastic Strain | b | Ellipse major axes |
BL-I | Bilinear isotropic hardening model of lattice core | e | Ellipse ratio |
BL-II | Bilinear isotropic hardening model of bottom and upper plates | Fmax | Maximum force |
EBM | Electron beam melting | xFmax | Deformation of the specimen at maximum force |
CT | Computed tomography | σmax | Maximum engineering stress |
aBCC | Length of BCC cell edge | εσmax | Strain at the maximum engineering stress |
l | Length of the struts in the multi-strut tensile specimen | E | Young’s Modulus |
d | Nominal lattice structure strut diameter | ET | Tangent Modulus |
t | Specimen’s upper plate thickness | YTS0.2% | Offset yield strength at strain 0.2% |
h | Height of the C-series specimens | UTS | Ultimate tensile strength |
hCAD | Nominal CAD height of the specimen | EIn | Initiating impact energy, energy just before impact |
tUpP | Thickness of the upper plate | vIn | Initiating speed, speed just before impact |
mC | Weight of the C-series specimens | m | Weight of the falling head |
mCAD_0.8 | CAD weight of the C-series specimen with nominal struts dimeter | tdef | Duration of deformation |
mCAD_0.95 | CAD weight of the C-series specimen with Gauss stuts diameter and real upper plate thickness | xDyn | Deformation of the specimens under dynamic loading |
Measured relative density of C-series | EAbs | Absorbed energy | |
CAD_0.8 | Calculated relative density of the CAD model with nominal diameter d = 0.8 mm | vUp | Speed of the rebound |
CAD_0.95 | Calculated relative density of the CAD model with measured Gaussian diameter d = 0.8 mm | kDyn | Average stiffness of the specimens under dynamic loading |
dgauss | Ideal struts Gauss cylinder | PAbs | Absorption power of the specimens under dynamic loading |
n | Number of the struts in the multi-strut specimen | hef | Effective length of the tensile specimen |
ρInd | deliberately increased density of the indenter to represent the weight of the whole falling head | Einp | Input energy to the current layer of the lattice structure |
SEM | Scanning electron microscopy | Elin | Linear energy—(laser power/laser speed) |
(Avg. Values) | Measured | CAD | |||||||
---|---|---|---|---|---|---|---|---|---|
h | tUpP | m | hCAD | mCAD_0.8 | mCAD_0.95 | CAD_0.8 | CAD_0.95 | ||
(mm) | (mm) | (g) | (%) | (mm) | (g) | (g) | (%) | (%) | |
21.04 | 0.75 | 6.97 | 31 | 20.80 | 4.72 | 6.94 | 21 | 31 |
(mm) | Corner Strut | dgauss | din | dout | Ellipse | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Minor Axis | Major Axis | ||||||||||
S1 | 1 | 0.94 | 0.95 | 0.74 | 0.73 | 1.26 | 1.21 | 0.79 | 0.79 | 1.1 | 1.12 |
2 | 0.99 | 0.75 | 1.19 | 0.81 | 1.17 | ||||||
3 | 0.93 | 0.7 | 1.24 | 0.79 | 1.14 | ||||||
4 | 0.93 | 0.72 | 1.16 | 0.78 | 1.09 | ||||||
S2 | 1 | 0.96 | 0.96 | 0.76 | 0.74 | 1.18 | 1.22 | 0.8 | 0.79 | 1.2 | 1.12 |
2 | 0.92 | 0.75 | 1.09 | 0.79 | 1.03 | ||||||
3 | 1.02 | 0.73 | 1.36 | 0.8 | 1.06 | ||||||
4 | 0.94 | 0.72 | 1.23 | 0.77 | 1.17 | ||||||
S3 | 1 | 0.86 | 0.91 | 0.69 | 0.71 | 1.08 | 1.18 | 0.78 | 0.76 | 1.08 | 1.06 |
2 | 0.91 | 0.69 | 1.26 | 0.77 | 1.05 | ||||||
3 | 0.94 | 0.76 | 1.2 | 0.76 | 1.13 | ||||||
4 | 0.91 | 0.7 | 1.17 | 0.73 | 0.97 | ||||||
S4 | 1 | 0.97 | 0.97 | 0.82 | 0.74 | 1.27 | 1.31 | 0.86 | 0.84 | 1.27 | 1.16 |
2 | 0.96 | 0.73 | 1.31 | 0.89 | 1.15 | ||||||
3 | 1.01 | 0.74 | 1.43 | 0.83 | 1.04 | ||||||
4 | 0.93 | 0.67 | 1.23 | 0.77 | 1.18 | ||||||
0.945 | 0.729 | 1.229 | 0.795 | 1.114 |
(mm) | TS45 | TS90 | TB45 | TB90 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
dgauss | din | dout | dgauss | din | dout | dgauss | din | dout | dgauss | din | dout | |
1 | 0.88 | 0.66 | 1.07 | 0.78 | 0.61 | 1.09 | 5.05 | 4.91 | 5.49 | 5.03 | 4.94 | 5.36 |
2 | 0.88 | 0.69 | 1.14 | 79 | 0.68 | 1.03 | 5.04 | 4.89 | 5.66 | 5.02 | 4.9 | 5.45 |
3 | 0.89 | 0.72 | 1.15 | - | - | - | 5.03 | 4.85 | 5.6 | 5.01 | 4.93 | 5.57 |
4 | 0.9 | 0.74 | 1.19 | 0.79 | 0.71 | 0.88 | - | - | - | - | - | - |
5 | 0.9 | 0.7 | 1.34 | 0.8 | 0.69 | 1.06 | - | - | - | - | - | - |
6 | 0.91 | 0.71 | 1.29 | 0.78 | 0.69 | 0.87 | - | - | - | - | - | - |
0.89 | 0.70 | 1.20 | 0.79 | 0.68 | 0.99 | 5.04 | 4.88 | 5.58 | 5.02 | 4.92 | 5.46 |
Spec. | Fmax (N) | xFmax (mm) | σmax (MPa) | εσmax | E (GPa) | YTS0.2% (MPa) | UTS (MPa) | ET (MPa) |
---|---|---|---|---|---|---|---|---|
TS45 | 2270 | 0.462 | - | 0.015 | 71.6 | 131.6 | 224.2 | 6649 |
TS90 | 1934 | 0.297 | - | 0.010 | 103.7 | 116.6 | 186.8 | 8701 |
TB45 | 7625 | 1.030 | - | 0.026 | 96.1 | 227.0 | 382.2 | 4858 |
TB90 | 6453 | 0.809 | - | 0.020 | 147.5 | 187.4 | 326 | 5753.3 |
C | 10,860 | 2.133 | 27.2 | 0.103 | 483.5 | - | - | - |
# | Fmax (N) | tdef (ms) | xDyn (mm) | vIn (m·s−1) | EIn (J) | EAbs (J) | vUp (m·s−1) | kDyn (N·mm−1) | PAbs (J·s−1) | |
---|---|---|---|---|---|---|---|---|---|---|
IT 0.6 | 4252 | 4.94 | 9.07 | 3.02 | 33.10 | 32.47 | 0.42 | 9005 | 6.58 | |
6479 | 4.64 | 7.67 | 2.95 | 31.51 | 31.19 | 0.30 | 6.73 | |||
4005 | 5.29 | 9.61 | 2.93 | 31.19 | 30.87 | 0.30 | 5.83 | |||
4660 | 5.04 | 8.86 | 2.95 | 31.48 | 31.20 | 0.28 | 6.19 | |||
6047 | 4.71 | 8.31 | 2.97 | 32.08 | 31.68 | 0.33 | 6.73 | |||
5089 | 4.92 | 8.70 | 2.96 | 31.87 | 31.48 | 0.32 | - | 6.41 | ||
IT 0.8 | - | - | - | - | - | - | - | - | - | |
9989 | 3.41 | 5.15 | 2.97 | 32.03 | 31.58 | 0.35 | 19,417 | 9.27 | ||
9368 | 4.05 | 6.00 | 2.93 | 31.91 | 31.71 | 0.24 | 7.82 | |||
12,218 | 2.94 | 4.32 | >2.96 | 31.87 | 31.31 | 0.39 | 10.66 | |||
9795 | 3.52 | 5.43 | 2.96 | 31.72 | 31.08 | 0.42 | 8.83 | |||
10,343 | 3.48 | 5.22 | 2.96 | 31.88 | 31.42 | 0.35 | - | 9.15 | ||
IT 1.0 | 15,223 | 2.79 | 3.83 | 3.07 | 34.22 | 33.89 | 0.30 | 29,371 | 12.14 | |
17,625 | 2.03 | 3.30 | 3.13 | 35.45 | 35.28 | 0.22 | 17.37 | |||
16,437 | 2.16 | 3.66 | 3.15 | 36.09 | 35.56 | 0.38 | 16.49 | |||
18,796 | 1.80 | 3.08 | 3.16 | 36.09 | 35.29 | 0.47 | 19.58 | |||
16,859 | 2.18 | 3.50 | 3.15 | 35.98 | 35.83 | 0.20 | 16.46 | |||
16,988 | 2.19 | 3.47 | 3.13 | 35.57 | 35.17 | 0.31 | - | 16.41 | ||
IT 1.2 | 24,205 | 1.49 | 2.43 | 3.19 | 36.93 | 34.87 | 0.75 | 39,006 | 23.41 | |
28,067 | 1.31 | 2.17 | 3.22 | 37.61 | 35.22 | 0.81 | 26.84 | |||
20,597 | 1.89 | 3.14 | 3.21 | 37.30 | 36.44 | 0.48 | 19.33 | |||
27,627 | 1.31 | 2.13 | 3.21 | 37.28 | 34.92 | 0.81 | 26.61 | |||
20,990 | 1.80 | 2.87 | 3.17 | 36.54 | 35.41 | 0.56 | 19.65 | |||
24,297 | 1.56 | 2.55 | 3.20 | 37.13 | 35.38 | 0.68 | - | 23.17 |
Parameters | BL-I (BCC) | BL-II (Plate) | Unit |
---|---|---|---|
Density | 2680 | 2680 | kg·m−3 |
Isotropic Elasticity | - | - | - |
Young’s Modulus | 70,723 | 96,100 | MPa |
Poisson’s Ratio | 0.334 | 0.334 | - |
Bulk Modulus | 7.1 × 1010 | 9.6 × 1010 | Pa |
Shear Modulus | 2.7 × 1010 | 3.6 × 1010 | Pa |
Bilinear Isotropic Hardening | - | - | - |
Yield Strength | 135 | 227 | MPa |
Tangent Modulus | 6586 | 4858 | MPa |
Plastic Strain Failure | - | - | - |
Max. Equivalent Plastic Strain EPS | 0.1025 | 0.1025 | - |
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Vrána, R.; Červinek, O.; Maňas, P.; Koutný, D.; Paloušek, D. Dynamic Loading of Lattice Structure Made by Selective Laser Melting-Numerical Model with Substitution of Geometrical Imperfections. Materials 2018, 11, 2129. https://doi.org/10.3390/ma11112129
Vrána R, Červinek O, Maňas P, Koutný D, Paloušek D. Dynamic Loading of Lattice Structure Made by Selective Laser Melting-Numerical Model with Substitution of Geometrical Imperfections. Materials. 2018; 11(11):2129. https://doi.org/10.3390/ma11112129
Chicago/Turabian StyleVrána, Radek, Ondřej Červinek, Pavel Maňas, Daniel Koutný, and David Paloušek. 2018. "Dynamic Loading of Lattice Structure Made by Selective Laser Melting-Numerical Model with Substitution of Geometrical Imperfections" Materials 11, no. 11: 2129. https://doi.org/10.3390/ma11112129