Material Selection Tutorial

Transcription

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

2 Ashby Material Selection Chart E MCH D Material Selection -

3 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. Select a quantity, Q, to minimize or maximize. Classify the variables. 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 * Based on N.E. Dowling, Mechanical Behavior of Materials, section.8 E MCH D Material Selection -

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

5 Step : 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 D Material Selection - 5

6 Step : 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 D Material Selection - 6

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

8 Step 5: Rank candidate materials based upon function f 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 D Material Selection - 8

9 Sample Problem We must bridge a gap of L 8 The bridge must have a width of b 4 A load P 00 lb can be applied at any point There must be a safety factor X.5 for strength The deflection, v, must not exceed Weight (mass) and cost have equal importance OBJECTIVE: select the best candidate material from AISI 00 steel AISI 440 steel 7075-T6 aluminum Ti-6Al-4V (titanium alloy) Polycarbonate Loblolly pine GFRP (glass fiber reinforced polymer) CFRP (carbon fiber reinforced polymer) E MCH D Material Selection - 9

10 Step : 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 D Material Selection - 0

11 Step : Classify the variables Requirements: L 8, b 4, P 00 lb, X.5, v Geometry: restrict analysis to a rectangular crosssection, h height Material Properties (need step 4 results here): ρ mass density, E Young s modulus, S strength, C m cost index E MCH D Material Selection -

12 Step : 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 D Material Selection -

13 b P h L Strength elastic flexural formula shows the maximum stress occurs at the extreme fibers of the beam at midspan Mc ( I PL ( 4, M h bh PLX S X( bh PL / 4, c h /, I bh PL bh PLX h bs Deflection from integration, is found to be maximum at midspan PL v 48EI PL 48Ebh PL 4Ebh / PL h 4Ebv E MCH D Material Selection -

14 E MCH D Material Selection - 4 Step 4: Determine Q as a function of requirements and material properties strength basis S C Xb PL m C C S Xb PL bs PLX bl bhl m m m Try using strength as the basis for material selection and then check deflection f

15 Step 5: Rank materials based upon function f strength basis Requirements L (in) 96 P (lb) 00 b (in) 4 X.5 v (in) Use spreadsheet to determine rankings Selection Table - strength basis (check deflection) Material Density Strength Cost f Norm Mass f Norm Cost (slug/in) (psi) Index for mass Mass Rank for cost Cost Rank AISI 00 steel 8.87E E E AISI 440 steel 8.87E E E T6 aluminum.0e E E Ti-6Al-4V 5.05E E E Polycarbonate.5E E E Loblolly pine 5.7E E E GFRP.5E E E CFRP.80E E E Material Q Combined Depth, h Modulus Deflection Stress Safety Check Rank (in) (psi) (in) (psi) Factor Deflection AISI 00 steel NG AISI 440 steel NG 7075-T6 aluminum NG Ti-6Al-4V NG Polycarbonate NG Loblolly pine NG GFRP NG CFRP NG E MCH D Material Selection - 5

16 E MCH D Material Selection - 6 Step 4: Determine Q as a function of requirements and material properties deflection basis E C v PL b m C C E v PL b Ebv PL bl bhl m m m Try using deflection as the basis for material selection and then check strength f

17 Step 5B: Rank materials based upon function f deflection basis Requirements L (in) 96 P (lb) 00 b (in) 4 X.5 v (in) Use spreadsheet to determine rankings Selection Table - deflection basis (check strength) Material Density Strength Cost f Norm Mass f Norm Cost (slug/in) (psi) Index for mass Mass Rank for cost Cost Rank AISI 00 steel 8.87E E E AISI 440 steel 8.87E E E T6 aluminum.0e E E-05.8 Ti-6Al-4V 5.05E E E Polycarbonate.5E E E Loblolly pine 5.7E E E GFRP.5E E E CFRP.80E E E Material Q Combined Depth, h Modulus Deflection Stress Safety Check Rank (in) (psi) (in) (psi) Factor Strength AISI 00 steel OK AISI 440 steel OK 7075-T6 aluminum OK Ti-6Al-4V OK Polycarbonate OK Loblolly pine OK GFRP OK CFRP OK E MCH D Material Selection - 7

18 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, 00 steel is second best, CFRP is worst E MCH D Material Selection - 8