Material Selection - Pennsylvania State University

Transcript Material Selection - Pennsylvania State University

Material Selection Tutorial

• Selecting an appropriate material is a critical part of almost all engineering designs • There are many factors to consider – Strength, stiffness, durability, corrosion, cost, formability, etc • Methods – Experience: how do you get it? limiting – Ashby selection charts ( http://www-materials.eng.cam.ac.uk/mpsite/DT.html

) – Quantitative ranking of options (described here) E MCH 213D Material Selection - 1

Ashby Material Selection Chart http://www-materials.eng.cam.ac.uk/mpsite/tutorial/non_IE/selchart.html

E MCH 213D Material Selection - 2

• • Quantitative Ranking of Options for Material Selection*

Objective

: develop a rational method to select the best material for an application based upon known material parameters and the requirements of the application Use a 5-step method 1. Select a quantity, Q, to minimize or maximize 2. Classify the variables 3. Determine the relationship between the geometry variable, the requirements, and material properties 4. Determine Q as a function of requirements and material properties 5. Rank candidate materials based upon function f 2 * Based on N.E. Dowling,

Mechanical Behavior of Materials

, section 3.8

E MCH 213D Material Selection - 3

Step 1: Select a quantity, Q, to minimize or maximize • Mass (weight), m • Cost, C are the most common and the only ones that we will consider E MCH 213D Material Selection - 4

Step 2: Classify the variables • Requirements – variables that have prescribed values that will not change • Geometry – variables that define the dimensions of the component and depend implicitly upon the material properties • Material Properties – variables used to define the material in terms of physical behavior, mechanical behavior, and cost E MCH 213D Material Selection - 5

Step 3: Determine the relationship between the geometry variable, the requirements, and material properties • Strength – Bar, axial stress – Beam, flexural stress • Stiffness – Bar, deformation – Beam, deflection E MCH 213D Material Selection - 6

Step 4: Determine Q as a function of requirements and material properties • Q = f 1 (requirements)* f 2 (material props) E MCH 213D Material Selection - 7

Step 5: Rank candidate materials based upon function f 2 • If both weight and cost are important then separate rankings can be generated and results combined • Calculate geometry variable after ranking materials – Adjustments may be necessary if calculated dimensions are impractical (either too large or too small) • There may be multiple requirements such as strength and serviceability – Often material can be selected based on strength and then the serviceability requirements checked E MCH 213D Material Selection - 8

Sample Problem

• We must bridge a gap of L = 8’ • The bridge must have a width of b = 4” • A load P = 300 lb can be applied at any point • There must be a safety factor X = 1.5 for strength • The deflection, v, must not exceed 1” • Weight (mass) and cost have equal importance OBJECTIVE: select the best candidate material from… AISI 1020 steel AISI 4340 steel 7075-T6 aluminum Polycarbonate Ti-6Al-4V (titanium alloy) Loblolly pine GFRP (glass fiber reinforced polymer) CFRP (carbon fiber reinforced polymer) E MCH 213D Material Selection - 9

Step 1: Select a quantity, Q, to minimize Here, mass and cost have equal importance • Mass, m • Cost, C Select Q to be the sum of the normalized mass and cost • Q = m/min(m) + C/min(C) E MCH 213D Material Selection - 10

Step 2: Classify the variables • Requirements: L = 8’, b = 4”, P = 300 lb, X = 1.5, v = 1” • Geometry: restrict analysis to a rectangular cross section, h = height • Material Properties (need step 3 & 4 results here): r = mass density, E = Young’s modulus, S = strength, C m = cost index E MCH 213D Material Selection - 11

Step 3: Determine the relationship between the geometry variable, the requirements, and material properties • We have a simply supported beam with a rectangular cross-section • The worst case occurs when the concentrated load, P, is applied at the center E MCH 213D Material Selection - 12

b P L h Strength – elastic flexural formula shows the maximum stress occurs at the extreme fibers of the beam at midspan  

M I



/ 4 ,



/ 2 ,



3 / 12  

PL h

4 12 2

3  3



  3

PLX

2 

   3

PLX

  1 2 Deflection – from integration, is found to be maximum at midspan



3 48

 12

3 48

Ebh

3 

3 4

Ebh

3 

  

3 4

Ebv

  1 3 E MCH 213D Material Selection - 13

Step 4: Determine Q as a function of requirements and material properties – strength basis Try using strength as the basis for material selection and then check deflection

 r

bhL

 r

  3

PLX

  1 2    3 2

  1 2   

r 1 2   



C m m

   3 2

  1 2    r

C m S

1 2    f 2 E MCH 213D Material Selection - 14

Step 5: Rank materials based upon function f 2 – strength basis

Requirements

L (in) = P (lb) = b (in) = X = v (in) = 96 300 4 1.5

1 Use spreadsheet to determine rankings

Selection Table - strength basis (check deflection)

Material Density (slug/in3) Strength (psi) Cost Index AISI 1020 steel AISI 4340 steel 7075-T6 aluminum Ti-6Al-4V 8.87E-03 8.87E-03 3.03E-03 5.05E-03 37708 159971 68020 171864 1 3 6 45 Polycarbonate Loblolly pine GFRP CFRP 1.35E-03 5.73E-04 2.25E-03 1.80E-03 8992 12763 55112 134880 5 1.5

10 200 f2 for mass 4.57E-05 2.22E-05 1.16E-05 1.22E-05 1.42E-05 5.07E-06 9.57E-06 4.89E-06 Norm Mass 9.34

4.53

2.38

2.49

2.90

1.04

1.96

1.00

Mass Rank 8 7 4 5 6 2 3 1 f2 for cost 4.57E-05 6.65E-05 6.98E-05 5.49E-04 7.11E-05 7.60E-06 9.57E-05 9.78E-04 Norm Cost 6.01

8.75

9.17

72.13

9.34

1.00

12.58

128.67

Cost Rank 2 3 4 7 5 1 6 8 Material AISI 1020 steel AISI 4340 steel 7075-T6 aluminum Ti-6Al-4V Polycarbonate Loblolly pine GFRP CFRP Q 15.35

13.28

11.55

74.63

12.25

2.04

14.54

129.67

Combined Depth, h Rank 6 (in) 0.655

4 2 7 3 0.318

0.488

0.307

1.342

1 5 8 1.127

0.542

0.347

Modulus (psi) 29441624 30021755 10297317 16968818 348078 1783901 3045685 11022480 E MCH 213D Deflection (in) 2.00

17.15

13.86

33.78

19.71

6.50

34.18

36.16

Stress (psi) 25139 106647 45347 114576 5995 8509 36742 89920 Safety Factor 1.50

1.50

Check Deflection NG NG NG NG NG NG NG NG Material Selection - 15

Step 4: Determine Q as a function of requirements and material properties – deflection basis Try using deflection as the basis for material selection and then check strength

m C

  r

bhL C m m

     r

  

3 4

Ebv

   1 3       r

1 3

C m

1 3       

2 4

   1 3   

r 1 3    f 2 E MCH 213D Material Selection - 16

Step 5B: Rank materials based upon function f 2 – deflection basis

Requirements

L (in) = P (lb) = b (in) = X = v (in) = 96 300 4 1.5

1 Use spreadsheet to determine rankings

Selection Table - deflection basis (check strength)

10 200 f2 for mass 2.87E-05 2.85E-05 1.39E-05 1.97E-05 1.92E-05 4.72E-06 1.55E-05 8.07E-06 Norm Mass 6.08

6.04

2.95

4.16

4.06

1.00

3.28

1.71

Mass Rank 8 7 4 6 5 1 3 2 f2 for cost 2.87E-05 8.56E-05 8.36E-05 8.85E-04 9.58E-05 7.08E-06 1.55E-04 1.61E-03 Norm Cost 4.06

12.09

11.81

124.93

13.52

1.00

21.87

227.96

Cost Rank 2 4 3 7 5 1 6 8 Material AISI 1020 steel AISI 4340 steel 7075-T6 aluminum Ti-6Al-4V Polycarbonate Loblolly pine GFRP CFRP Q 10.14

18.13

14.76

129.10

17.58

2.00

25.16

229.67

Combined Depth, h Rank 2 (in) 0.826

5 3 7 4 0.821

1.172

0.992

3.626

1 6 8 2.103

1.759

1.146

Modulus (psi) 29441624 30021755 10297317 16968818 348078 1783901 3045685 11022480 Deflection (in) 1.00

1.00

Stress (psi) 15831 16039 7859 10964 822 2442 3489 8224 E MCH 213D Safety Factor 2.38

9.97

8.66

15.67

10.94

5.23

15.80

16.40

Check Strength OK OK OK OK OK OK OK OK Material Selection - 17

Sample Problem Results

• Material selection based only on strength results in the deflection criterion being violated • Material selection based only on deflection results in the strength criterion being satisfied • We can say that deflection governs this design • Pine is best, 1020 steel is second best, CFRP is worst E MCH 213D Material Selection - 18

Material Selection - Pennsylvania State University

Transcript Material Selection - Pennsylvania State University

Material Selection Tutorial

Sample Problem

Sample Problem Results

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