Page 82 - MSAM-3-3

Materials Science in Additive Manufacturing Gradient porous material design criteria

Table 3. Energy absorption until the first load drop/elastic limit  d  15.
.
of Gyroid‑sheet and Diamond‑sheet uniform porosity materials σ = σ ×1 0822   (16)
ys
y
 d s 
Porosity Energy absorption Energy absorption
(%) until the first load until the elastic
2
drop (MJ/m ) limit (MJ/m ) W = 0.0128ρ - 2.7672 ρ + 148.1761 (17)
3
3
uρ
Schon-Gyroid-sheet uniform porosity materials W = 0.0034ρ - 0.6836ρ + 34.2847 (18)
2
50 41.95±1.33 8.36±0.13 e
2
60 27.57±3.56 5.82±0.32 W = 0.0123ρ - 2.4737ρ + 127.3302 (19)
uρ
70 18.46±1.35 3.41±0.45 W = 0.0042ρ - 0.8112ρ + 40.2703 (20)
2
80 7.73±0.69 1.04±0.12 e
90 3.12±0.07 0.88±0.09 where d is the relative density of the porous materials;
Schwarz-Diamond-sheet uniform porosity materials d is the relative density of the solid materials; σ is the
y
s
50 34.44±1.23 10.45±0.56 yield stress of the porous materials; σ is the yield stress
ys
60 22.89±2.64 6.92±0.32 of the solid materials; W is the energy absorption until
uρ
70 14.41±1.03 4.05±0.11 the first load drop; W is the energy absorption until the
e
80 8.14±0.64 2.63±0.12 elastic limit, and ρ is the porosity. Since all terms are
90 4.08±0.12 1.49±0.07 obtained, the coefficient C can be calculated according to
Equation 14, as shown in Table 4. For the Schon-Gyroid-
sheet gradient porosity materials, the coefficient C is
1.0715, and coefficient C is 1.0976 for Schon-Diamond-
sheet gradient porosity materials. Hence, Equation 14
can be transformed to as Equation 21 for Schon-Gyroid-
sheet gradient porosity materials and Equation 22 for
Schwarz-Diamond-sheet gradient porosity materials.
W g = ρ σε + d ρ ∫ 1 ε 1 ρ ε σεd ρ ∫ 0 2 + 0 ε ρ2 3 σεd ρ ∫ 0 13 + 1.0715
 (σ σ + )  ∆ ρ l  
 1 y y 2 × 12 ×  1  
 2  ( − ρ 1 ) +∆ ρ l    
 1 12 0 
  (σ + σ )  
×− ε 2 σε y 2 + y 2 y 3 × (21)
d
y

 2  ∫ 0 
 ∆ ρ ( + l )   
'
l
 23 × 1 2   − ε 3 y σε  d
Figure 12. Stress-strain curves of Gyroid-sheet and Diamond-sheet  (   − ρ 1 2 ) +∆ ρ 23 l 0   ∫ 0 y 3 
gradient porosity materials with the design of 60 – 70 – 80% (2/2/2)    
A B

Figure 13. Gibson and Ashby model for yield stress of Gyroid-sheet (A) and Diamond-sheet uniform porosity materials (B)

Volume 3 Issue 3 (2024) 11 doi: 10.36922/msam.4234