Material selection

1. MATERIAL SELECTION
( shelf & front cover )
Product Development Studio
GROUP 9

2. FOR SHELF

3. density of paper: ρ=1.25g/cm3
size of magazine=21cm*29cm
width of shelf=36cm
∴Total force: F=mg=ρ*V*g=1.25g/cm3
* (21cm * 29cm * 36cm) * 9.8N/kg = 268.57N
∵2N=F
∴N=134.28N
∴P=268.57N/36cm=746N/m
M(max) = 134.28N*18cm – 134.28N*9cm = 12N*m
σ(max) = ((12N*m) * (h/2))/((0.25m*h3
)/12) = 288/h2
Pa
∴288/h2
Pa <σy
∵Deformation=FL3
/(384/5 * E* bh3
/12) ≤ 5% * L
∴E≥435/h3
Pa
In sum, we have two constrains:
σy > 288/h2
Pa
E > 435/h3
Pa
And if we use extrusion manufacture method:
We can check the range of section thickness for extrusion is:

4. So, let us try from the thickmost one: Try h= 6mm, means
σy > 288/(6mm)2
Pa
E > 435/(6mm)3
Pa
σy > 8 MPa
E≥ 2GPa
Then we set limits in CES:
Set limits in durability(water and sunshine)
We can see there are five candidates:

5. We check them one by one:
1. Polyvinylchloride(tpPVC)
The maximum E is 4.14GPa, the maximum σy is 52.1MPa.
52.1 > 288/h2
4.14 > 435/h3
H > 2.3511mm
H > 4.72mm
∴H(min) = 4.7mm
Mass=ρ * V =ρ * (A*5mm) = (1300~1580) * (A*4.7mm) = (6.11~7.43) A
Cost = (1.12~1.23) (6.11~7.43) A =（6.84~9.14）A
2. Polylactide(PLA)
The maximum E is 3.83GPa, the maximum σy is 60MPa.
60 > 288/h2
3.83 > 435/h3

6. H > 2.19mm
H > 4.843mm
∴H(min) = 4.9mm
Mass=ρ * V =ρ * (A*5mm) = (1210~1250) * (A*4.9mm) = (5.93~6.13) A
Cost = (1.75~2.11) (5.93~6.13) A =（10.38~12.93）A
3. Polyethylene terephthalate(PET)
The maximum E is 4.14GPa, the maximum σy is 62.3MPa.
62.3 > 288/h2
4.14 > 435/h3
H > 2.15mm
H >4.72mm
∴H(min) = 4.7mm
Mass=ρ * V =ρ * (A*4.7mm) = (1290~1400) * (A*4.7mm) = (6.06~6.58) A
Cost = (1.65~1.82) (6.06~6.58) A =（10.00~11.98）A

7. 4. Polymethyl methacrylate (Acrylic, PMMA)
The maximum E is 3.8GPa, the maximum σy is 72.4MPa.
72.4 > 288/h2
3.8 > 435/h3
H > 1.99mm
H >4.86mm
∴H(min) = 4.9mm
Mass=ρ * V =ρ * (A*4.9mm) = (1160~1220) * (A*4.9mm) = (5.68~5.98) A
Cost = (2.19~2.41) (5.68~5.98) A =（12.44~14.41）A
5. Polyetheretherketone (PEEK)
The maximum E is 3.95GPa, the maximum σy is 95MPa.
95 > 288/h2
3.95 > 435/h3

8. H > 1.74mm
H >4.79mm
∴H(min) = 4.8mm
Mass=ρ * V =ρ * (A*4.8mm) = (1300~1320) * (A*4.8mm) = (6.24~6.34) A
Cost = (78.9~86.8) (6.24~6.34) A =（492.34~550.31）A
Then, we compare the five candidates, they are:
1. Polyvinylchloride(tpPVC)
Mass = (6.11~7.43) A
Cost =（6.84~9.14）A
2. Polylactide(PLA)
Mass = (5.93~6.13) A
Cost =（10.38~12.93）A
3. Polyethylene terephthalate(PET)
Mass = (6.06~6.58) A
Cost =（10.00~11.98）A
4. Polymethyl methacrylate (Acrylic, PMMA)
Mass = (5.68~5.98) A
Cost =（12.44~14.41）A
5. Polyetheretherketone (PEEK)
Mass = (6.24~6.34) A
Cost =（492.34~550.31）A

9. So, we can see from the above picture the three proper candidates are Polyvinylchloride(tpPVC),
Polylactide(PLA) and Polymethyl methacrylate(Acrylic, PMMA).
Then we check the three in level 3, firstly let us start from Polyvinylchloride(tpPVC):
1. Polyvinylchloride(tpPVC)
We can see there are five sub-candidates in Polyvinylchloride(tpPVC):
Then we try them one by one:

10. 1. PVC(rigid, high impact, molding and extrusion)
The maximum E is 3.1GPa, the maximum σy is 45.5MPa.
45.5 > 288/h2
3.1 > 435/h3
H > 2.52mm
H >5.2mm
∴H(min) = 5.2mm
Mass=ρ * V =ρ * (A*5.2mm) = (1290~1460) * (A*5.2mm) = (6.71~7.59) A
Cost = (1.93~2.13) (6.71~7.59) A =（12.95~16.17）A
2. PVC(20% glass fiber, molding)
The maximum E is 6.69GPa, the maximum σy is 70.6MPa.
70.6 > 288/h2
6.69 > 435/h3
H > 2.02mm
H >4.02mm
∴H(min) = 4mm
Mass=ρ * V =ρ * (A*4mm) = (1430~1500) * (A*4mm) = (5.72~6) A
Cost = (5.72~6) A (1.91~2.22) =（10.93~13.32）A

11. 3. PVC(chlorinated, molding and extrusion)
The maximum E is 3.41GPa, the maximum σy is 58MPa.
58 > 288/h2
3.41 > 435/h3
H > 2.23mm
H >5.03mm
∴H(min) = 5mm
Mass=ρ * V =ρ * (A*5mm) = (1450~1560) * (A*5mm) = (7.25~7.8) A
Cost = (7.25~7.8) A (2.21~2.42) =（16.02~18.88）A
4. PVC(rigid, molding and extrusion)
The maximum E is 3.3GPa, the maximum σy is 52.7MPa.
52.7 > 288/h2
3.3 > 435/h3
H > 2.34mm
H >5.09mm
∴H(min) = 5mm
Mass=ρ * V =ρ * (A*5mm) = (1300~1490) * (A*5mm) = (6.5~7.45) A
Cost = (6.5~7.45) A (1.12~1.23) =（7.28~9.16）A

12. 5. PVC(rigid, lead stabilized)
The maximum E is 2.4GPa, the maximum σy is 43.4MPa.
43.4 > 288/h2
2.4 > 435/h3
H > 2.58mm
H >5.66mm
H(min) = 5.7mm
Mass=ρ * V =ρ * (A*6mm) = (1380~1400) * (A*5.7mm) = (7.87~7.98) A
Cost = (1.12~1.23) (7.87~7.98) A =（8.81~9.82）A
Then, we check Polylactide(PLA) in level 3 to see its sub-candidates
2. Polylactide(PLA)
After setting the limits, we can see there is only one candidates:

13. The candidate is just Polyactide(PLA):
The maximum E is 3.83GPa, the maximum σy is 60MPa.
60 > 288/h2
3.83 > 435/h3
H > 2.19mm
H > 4.843mm
∴H(min) = 4.9mm
Mass=ρ * V =ρ * (A*5mm) = (1210~1250) * (A*4.9mm) = (5.93~6.13) A
Cost = (1.75~2.11) (5.93~6.13) A =（10.38~12.94）A
Then, we check Polymethyl methacrylate(Acrylic, PMMA) in level 3 to see its sub-candidates
3. Polymethyl methacrylate(Acrylic, PMMA)
After setting the limits, we find there are four candidates: PMMA(cast sheet), PMMA(heat
resistant), PMMA(impact modified) and PMMA(molding and extrusion)

14. 1. PMMA(cast sheet)
The maximum E is 2.9GPa, the maximum σy is 63.7MPa.
63.7 > 288/h2
2.9 > 435/h3
H > 2.13mm
H > 5.31mm
∴H(min) = 5.3mm
Mass=ρ * V =ρ * (A*5.3mm) = (1180~1200) * (A*5.3mm) = (6.25~6.36) A
Cost = (2.19~2.41) (6.25~6.36) A =（13.69~15.33）A
2. PMMA(heat resistant)
The maximum E is 3.8GPa, the maximum σy is 72.4MPa.
72.4 > 288/h2
3.8 > 435/h3
H > 1.99mm
H > 4.86mm
∴H(min) = 4.9mm
Mass=ρ * V =ρ * (A*4.9mm) = (1160~1220) * (A*4.9mm) = (5.68~5.98) A
Cost = (2.19~2.41) (5.68~5.98) A =（12.44~14.41）A

15. 3. PMMA(impact modified)
The maximum E is 3.3GPa, the maximum σy is 58.4MPa.
58.4 > 288/h2
3.3 > 435/h3
H > 2.22mm
H > 5.09mm
∴H(min) = 5mm
Mass=ρ * V =ρ * (A*5mm) = (1110~1180) * (A*5mm) = (5.55~5.9) A
Cost = (5.55~5.9)A(2.99~3.28) =（16.59~19.35）A
4. PMMA(molding and extrusion)
The maximum E is 3.24GPa, the maximum σy is 72.4MPa.
72.4 > 288/h2
3.24 > 435/h3
H > 1.99mm
H > 5.12mm
∴H(min) = 5.1mm
Mass=ρ * V =ρ * (A*5mm) = (1170~1200) * (A*5.1mm) = (5.97~6.12) A
Cost = (2.19~2.41) (5.97~6.12) A =（13.07~14.75）A

16. Then, we compare these candidates:
The best two candidates are PVC(rigid, molding and extrusion) and PVC(20% glass fiber,
molding), we need to exam them two again.
A = 36cm2
* 24cm2
= 864cm2
= 0.0864m2
PVC(rigid, molding and extrusion)
Mass=ρ * V =ρ * (A*5mm) = (1300~1490) * (A*5mm) = (6.5~7.45) A = (0.56~0.64) kg
Cost = (6.5~7.45) A (1.12~1.23) =（7.28~9.16）A = (0.63~0.79) euro
Mass(average) = 0.6 kg
Cost(average) = 0.61 euro
PVC(20% glass fiber, molding)
Mass=ρ * V =ρ * (A*4mm) = (1430~1500) * (A*4mm) = (5.72~6) A = (0.49~0.52) kg
Cost = (5.72~6) A (1.91~2.22) =（10.93~13.32）A = (0.94~1.15) euro
Mass(average) = 0.515 kg
Cost (average)= 1.545 euro
Then, we make a chart to compare them:
(let us assume cost and mass have the same importance value)
Firstly, we see the relationship between number and its score

17. We can see that the bigger the mass (or cost), the smaller the score.
Then we put the above two candidates into these two graph:
The score of PVC(rigid, molding and extrusion) is 4+6.95=10.95
The score of PVC(20% glass fiber, molding) is 4.85+2.275=7.125
∴It’s obvious that PVC(rigid, molding and extrusion) is better.

18. FOR FRONT SHELL
Manufacture method: Injection Molding
We can check the thickness range for injection molding, we can see the biggest thickness is 6mm
The suitable force range: 90N~120N
The suitable deformation: 3mm~6mm
Consider the dangerous point,
M(max) =F* 0.02m
σ(max) = ((F*0.02m)*(h/2))/( (b*h3
)/12)
if b=0.02m
σ(max) = 6F/ h2
∴σy >6F/ h2
means σy >(6F/ h2
)max
∴σy >6*120/ h2
= 720/ h2

19. F/D=3EI/L3
= E h3
/0.02*0.08
∵3mm < D < 6mm
∴0.003m < 0.02*0.08*F/Eh3
< 0.006m
1.6F/ 6h3
< E < 1.6F/ 3h3
means (1.6F/ 6h3
) max< E < (1.6F/ 3h3
) min
∴1.6*120/ 6h3
< E < 1.6*90/ 3h3
∴32/ h3
< E < 48/h3
In sum, the constrain: ①σy >720/ h2
②32/ h3
< E < 48/h3
32/ h3
< E < 48/h3
 (32/E)1/3
< h <(48/E)1/3

20. If h=6mm
σy >20Mpa
0.148GPa < E < 0.222GPa
If h=1mm
σy >720Mpa
32GPa < E < 48GPa
So, the whole range is
0.148GPa < E < 48GPa
Then, we set limits in CES level 3 (because in level 2 there are no survivors)
We find there are 7 candidates:
They are ⑴ETFE(unfilled) ⑵PE-UHMW(molding and extrusion) ⑶PP(copolymer, UV
stabilized) ⑷PVC/PMMA(unfilled) ⑸PVDC(copolymer, injection) ⑹PVDF(copolymer,
wire and cable jacketing) ⑺PVDF(homopolymer, molding and extrusion).
We check them one by one:

21. 1. ETFE(unfilled)
(32/E)1/3
< h <(48/E)1/3
(32/0.848)1/3
< h <(48/0.807)1/3
3.354mm<h<3.904mm
∴h(min)=3.4mm
Mass = (1680~1720)(A*3.4mm)=(5.71~5.85)A
Cost=mass*Price=(5.71~5.85)(21.1~30.3)=(120.48~177.256)A
2. PE-UHMW(molding and extrusion)
(32/E)1/3
< h <(48/E)1/3
(32/0.963)1/3
< h <(48/0.894)1/3
3.215mm<h<3.773mm
∴h(min)=3.3mm
Mass = (931~949)(A*3.3mm)=(3.07~3.13)A
Cost=mass*Price=(3.07~3.13)(2.1~2.32)=(6.45~7.26)A
3. PP(copolymer, UV stabilized)
(32/E)1/3
< h <(48/E)1/3
(32/1.26)1/3
< h <(48/1.23)1/3
2.939mm<h<3.392mm
∴h=3mm

22. Mass = (899~909)(A*3mm)=(2.70~2.73)A
Cost=mass*Price=(2.697~2.727)(1.53~1.76)=(4.13~4.80)A
4. PVC/PMMA(unfilled)
(32/E)1/3
< h <(48/E)1/3
(32/2.55)1/3
< h <(48/2.34)1/3
2.324mm<h<2.737mm
∴h=2.4mm
Mass = (1260~1350)(A*2.4mm)=(3.02~3.24)A
Cost=mass*Price = (3.02~3.24)(2.25~2.47)=(6.80~8.00)A
5. PVDC(copolymer, injection)
(32/E)1/3
< h <(48/E)1/3
(32/0.552)1/3
< h <(48/0.345)1/3
3.87mm<h<5.18mm
∴h=3.9mm
Mass = (1650~1720)(A*3.9mm)=(4.98~6.71)A
Cost=mass*Price = (4.98~6.71)(2.99~3.3)=(14.89~22.14)A
6. PVDF(copolymer, wire and cable jacketing)
(32/E)1/3
< h <(48/E)1/3
(32/1.31)1/3
< h <(48/1)1/3

23. 2.90mm<h<3.63mm
∴h=2.9mm
Mass = (1760~1770)(A*2.9mm)=(5.10~5.13)A
Cost=mass*Price = (5.10~5.13)(12.6~13.9)=(64.26~71.31)A
7. PVDF(homopolymer, molding and extrusion)
(32/E)1/3
< h <(48/E)1/3
(32/2.5)1/3
< h <(48/2)1/3
2.34mm<h<2.88mm
∴h=2.4mm
Mass = (1770~1780)(A*2.4mm)=(4.25~4.27)A
Cost=mass*Price = (4.25~4.27)(12.6~13.9)=(53.55~59.35)A

24. Then we compare them:
1. ETFE(unfilled)
Mass = (5.71~5.85)A
Cost = (120.48~177.256)A
2. PE-UHMW(molding and extrusion)
Mass = (3.07~3.13)A
Cost = (6.45~7.26)A
3. PP(copolymer, UV stabilized)
Mass = (2.70~2.73)A
Cost = (4.13~4.80)A
4. PVC/PMMA(unfilled)
Mass = (3.02~3.24)A
Cost = (6.80~8.00)A
5. PVDC(copolymer, injection)
Mass = (4.98~6.71)A
Cost = (14.89~22.14)A
6. PVDF(copolymer, wire and cable jacketing)
Mass = (5.10~5.13)A
Cost = (64.26~71.31)A
7. PVDF(homopolymer, molding and extrusion)
Mass = (4.25~4.27)A
Cost = (53.55~59.35)A
-
It is obvious that PP(copolymer, UV stabilized) is the best material.

25. Finally,