Figure 1.
(a) Shape of unit cell before homogenization. (b) Shape of unit cell after homogenization.
Figure 2.
Shape of orthotropic elasticity.
Figure 3.
The shape of circular pores. (a) Isotropic view. (b) Top view.
Figure 4.
The shape of elliptical pores. (a) Isotropic view. (b) Top view.
Figure 5.
Dimension and distribution of circular pores (Reprinted from Ref. [
13]).
Figure 6.
Dimension and distribution of elliptical pores (Reprinted from Ref. [
14]).
Figure 7.
(a) Shape of optical microscope. (b) Image with optical microscope.
Figure 8.
The shape of unit cell. (a) Circular pore. (b) Elliptical pore.
Figure 9.
The procedure of calculation of equivalent mechanical properties.
Figure 10.
The shape of unit cell after meshing. (a) Circular pores. (b) Elliptical pores.
Figure 11.
The boundary condition for strain. (a) X-direction tensile strain. (b) XY-direction shear strain.
Figure 12.
The distribution of stress with 0.1% strain condition. (a) X-direction tensile strain. (b) XY-direction shear scheme 11. S22, S33, S12, S13 and S23 (S11: tensile stress of X-direction, S22: tensile stress of Y-direction, S33: tensile stress of Z-direction, S12: shear stress of XY-direction, S13: shear stress of XZ-direction, S23: shear stress of YZ-direction) of each element were calculated and printed out. The calculation of weighted average concluded the equivalent stress of each direction at each step.
Figure 12.
The distribution of stress with 0.1% strain condition. (a) X-direction tensile strain. (b) XY-direction shear scheme 11. S22, S33, S12, S13 and S23 (S11: tensile stress of X-direction, S22: tensile stress of Y-direction, S33: tensile stress of Z-direction, S12: shear stress of XY-direction, S13: shear stress of XZ-direction, S23: shear stress of YZ-direction) of each element were calculated and printed out. The calculation of weighted average concluded the equivalent stress of each direction at each step.
Figure 13.
(a) UTM. (b) Two-axis strain gauge.
Figure 14.
Types of test specimens. (
a) Specimen with circular pores. (
b) Specimen with elliptical pores—long axis in the tensile direction. (
c) Specimen with elliptical pores—short axis in the tensile direction (Reprinted from Ref. [
14]).
Figure 14.
Types of test specimens. (
a) Specimen with circular pores. (
b) Specimen with elliptical pores—long axis in the tensile direction. (
c) Specimen with elliptical pores—short axis in the tensile direction (Reprinted from Ref. [
14]).
Figure 15.
Stress–strain curve for circular pores (Type I).
Figure 16.
Stress–strain curve for elliptical pores. (a) Type II. (b) Type III.
Figure 17.
The shape of imperfect fabrication.
Table 1.
Comparison of design proposal and actual results (unit: μm).
| Design | Real |
---|
Circular pore | Length of unit cell | 220.0 | 221.25 |
Hole diameter | 120.0 | 116.25 |
Elliptical pore | Length of unit cell | 440.0 | 433.13 |
Hole diameter | Short | 120.0 | 120.00 |
Long | 240.0 | 233.13 |
Table 2.
Mechanical properties of SUS304 [
13,
14].
Contents | Value | Unit |
---|
Density | 8000 | kg/m3 |
Modulus of elasticity | 193.0 | GPa |
Poisson’s ratio | 0.29 | - |
Table 3.
Equivalent properties with simulation for circular pores.
Contents | Value | Unit |
---|
Elastic modulus (Ex) | 112.3 | GPa |
Elastic modulus (Ey) | 112.3 | GPa |
Elastic modulus (Ez) | 147.9 | GPa |
Poisson’s ratio (νyx) | 0.230 | m/m |
Poisson’s ratio (νxy) | 0.230 | m/m |
Poisson’s ratio (νzx) | 0.290 | m/m |
Poisson’s ratio (νzy) | 0.290 | m/m |
Table 4.
Equivalent properties with simulation for elliptical pores.
Contents | Value | Unit |
---|
Elastic modulus (Ex) | 106.2 | GPa |
Elastic modulus (Ey) | 127.6 | GPa |
Elastic modulus (Ez) | 150.5 | GPa |
Poisson’s ratio (νyx) | 0.235 | m/m |
Poisson’s ratio (νxy) | 0.196 | m/m |
Poisson’s ratio (νzx) | 0.290 | m/m |
Poisson’s ratio (νzy) | 0.290 | m/m |
Table 5.
Equivalent properties of Specimen Type I [
13].
Test No. | Modulus of Elasticity (GPa) | Poisson’s Ratio (mm/mm) |
---|
1 | 116.0 | 0.226 |
2 | 117.0 | 0.228 |
3 | 117.0 | 0.243 |
4 | 118.0 | 0.248 |
5 | 118.0 | 0.242 |
6 | 117.0 | 0.231 |
Average | 117.17 | 0.2363 |
Standard Deviation | 0.687 | 0.0083 |
Table 6.
Equivalent properties of Specimen Type II [
14].
Test No. | Modulus of Elasticity (GPa) | Poisson’s Ratio (mm/mm) |
---|
1 | 124.0 | 0.211 |
2 | 124.0 | 0.233 |
3 | 124.0 | 0.212 |
4 | 127.0 | 0.223 |
5 | 123.0 | 0.219 |
6 | 122.0 | 0.226 |
Average | 124.0 | 0.221 |
Standard Deviation | 1.53 | 0.0077 |
Table 7.
Equivalent properties of Specimen Type III [
14].
Test No. | Modulus of Elasticity (GPa) | Poisson’s Ratio (mm/mm) |
---|
1 | 110.0 | 0.196 |
2 | 109.0 | 0.196 |
3 | 111.0 | 0.188 |
4 | 110.0 | 0.206 |
5 | 109.0 | 0.194 |
6 | 109.0 | 0.199 |
Average | 109.7 | 0.197 |
Standard Deviation | 0.75 | 0.0054 |
Table 8.
Difference between simulation and measurement for Type I.
| Modulus of Elasticity (GPa) | Poisson’s Ratio (mm/mm) |
---|
Simulation | 112.3 | 0.232 |
Measurement | 117.2 | 0.236 |
Difference (%) | 4.18 (%) | 1.69 (%) |
Table 9.
Difference between simulation and measurement for Type II.
| Modulus of Elasticity (Ey, GPa) | Poisson’s Ratio (νyx, m/m) |
---|
Simulation | 127.6 | 0.236 |
Measurement | 124.0 | 0.221 |
Difference (%) | 2.82 (%) | 6.36 (%) |
Table 10.
Difference between simulation and measurement for Type III.
| Modulus of Elasticity (Ex, GPa) | Poisson’s Ratio (νxy, m/m) |
---|
Simulation | 106.2 | 0.196 |
Measurement | 109.7 | 0.197 |
Difference (%) | 3.19 (%) | 0.51 (%) |