Modernization of two cycles (MA, BA) of competence-based curricula in Material Engineering according to the best experience of Bologna Process An introduction to the possibilities of Materials Selection. Prof Dr ir Jan Ivens Jan.ivens@kuleuven.be
2 Content Introduction The steps in materials selection Example: the underbody plate of a car
The Materials Library
Dependence on Non-renewable Materials 4
5 A CAR
6 A light car
7 A cheap car
8 An environmentally friendly car
9 The design process
10 Steps
11
12 Brainstorm Gather: o o What is the purpose of the component? function? What can all play a role in the materials selection? No restrictions Assess: what is important? What is not? o o o Need to have: primary elements Nice to have: secondary Others What is our design focus (goal)?
1 Translation s ranking screening
14 Our car: function
15 Objectives Minimise weight/cost/environmental impact of bottom plate of car w t L
16 Objective 1: minimize mass m = ρ L w t 10000 Osmium, commercial purity, hard Gold-Cu-Ag alloy, soft, wire, 1mm dia. (dental alloy) Cast iron, austenitic (flake), former BS L-NiCr 20 2 Low alloy steel, AISI 9255, tempered at 15 C & oil quenched Polyester SMC (0% glass fibre, slow-burning, low de Titanium, alpha-beta alloy, Ti-6Al-2Sn-4Zr-6Mo (6-2-4-6) Aluminum, 7050, wrought, T7452 Massaranduba (t) Density (kg/m^) 1000 Polyester (glass fiber, preformed, chopped glass) Concrete (insulating lightweight) Satinwood (l) Kempas (l) 100 PVC cross-linked foam (rigid, closed cell, DH 0.100) 10 Melamine foam (0.011)
17 Objective 2: minimize material cost 1e6 C = = C C m m m ρ L w t 100000 10000 Diamond Rhodium, commercial purity, hard Platinum-rhodium alloy, annealed, 40%Rh 1000 Al-47%SiC(f), transverse Price (GBP/kg) 100 10 Glass/polyimide honeycomb, ±45 fabric (0.072), L Direction Elm (ulmus rubra) (l) 1 Pine (pinus caribaea) (l) 0.1 0.01 Polyethylene terephthalate foam (closed cell, 0.2) Cement bonded particle board, perpendicular to board Asphalt concrete
18 Constraint 1 => Limited elastic deformation S F = δ EI C 1 L I = wt 12 F w t L
19 Constraint 2 => No plastic deformation or failure FL FL σ = C Z = C' wt 2 σ f F w t L
20 Constraint => No brittle fracture K Ic K = Y σ π a Maximum = yield strength Determined by defect detection limit
21 Simplest case Simplest case: Design with multiple constraints Design with Design one objective, with multiple meeting objectives a single constraint Function One Objective: one the performance metric metric Multiple Objectives: several performance metrics One Constraint Many Constraints One Constraint Many Constraints Rank by performance metric Rank by most most restrictive restrictive performance metric Penalty Trade-off and function value function method Combination of methods
22 Free variable(s) L & w are determined by car dimensions => constants t (thickness of bottom plate) can be varied => free variable
2 Case 1 A light car stiffness constraint Eliminate the free variable by combining objective and constraint function m = ρ x L x w x t Load S F = δ C 1 E I L m 2 12w L C 1 2 F δ ρ E I = t w 12 Geometry Material Properties
24 Material Index MI MI = ρ min Log(E)-log(ρ) = log(mi ) E E Log(E) = log(ρ) + log(mi ) MI ' = ρ max Y = mx +Q Slope =
25 Material Index Slope =
26 List of Materials Passing FOAMS and WOOD!
27 Case 2 A cheap car strength constraint Eliminate the free variable by combining objective and constraint function C = Cm ρ L w t FL σ f C' wt 2 C C' w L Geometry Load F C m σ ρ Material Properties f
28 Material Index C m C σ σ m ρ f f ρ min max Log(σ f )-2log(C m ρ) = 2log(MI) Log(σ f ) = 2log(C m ρ) + 2log(MI) Y = mx +Q Slope = 2
29 Slope = 2
0 List of materials passing Name Stage 2: Index Aerated concrete 0,029 Hardboard (tempered), perpendicular to board 0,0242 Hardboard (standard), perpendicular to board 0,0216 Concrete (structural lightweight) 0,0216 Redwood (sequoia sempervirens (young)) (l) 0,0215 Hardboard (tempered), parallel to board 0,0214 Fir (abies procera) (l) 0,0206 Spruce (picea rubens) (l) 0,0198 Oak (quercus falcata var. pagodifolia) (l) 0,0197 Spruce (picea abies) (l) 0,0191 Fiberboard, hard, perpendicular to board 0,0191 Plywood ( ply, beech), parallel to face layer 0,019 Plywood (5 ply, beech), parallel to face layer 0,019 Plywood (7 ply, beech), parallel to face layer 0,019 Fiberboard, extra hard, perpendicular to board 0,0188 Pine (pinus spp.) (l) 0,0185 Douglas fir (pseudotsuga menziesii (northern)) (l) 0,0182 Larch (larix decidua) (l) 0,0177 Concrete (super sulfate cement) 0,0169 WOOD and CONCRETE
1 Case A cheap car no brittle fracture Eliminate the free variable by combining objective and constraint function C = Cm ρ L w t K Ic Yσ πa C YC' w L πa Load F C m K ρ Ic σ = C FL ' wt 2 Geometry Material Properties
2 Material Index C ρ C m K K Ic Ic mρ min max Log(Κ Ic )-2log(C m ρ) = 2log(MI) Log(Κ Ic ) = 2log(C m ρ) + 2log(MI) Y = mx +Q Slope = 2
Slope = 2
4 List of materials passing Name Stage 2: Index Aerated concrete 0,029 Hardboard (standard), perpendicular to board 0,0216 Redwood (sequoia sempervirens (young)) (l) 0,0215 Fir (abies procera) (l) 0,0206 Spruce (picea rubens) (l) 0,0198 Oak (quercus falcata var. pagodifolia) (l) 0,0197 Spruce (picea abies) (l) 0,0191 Pine (pinus spp.) (l) 0,0185 Larch (larix decidua) (l) 0,0177 Concrete (super sulfate cement) 0,0169 Wood chipboard, type C1, parallel to board 0,0167 Wood chipboard, type C1A, parallel to board 0,0159 Wood chipboard, type C, parallel to board 0,0158 Gypsum bonded particleboard, parallel to board 0,0156 Wood chipboard, type C1, perpendicular to board 0,0152 Wood chipboard, type C1A, perpendicular to board 0,0145 Wood chipboard, type C, perpendicular to board 0,0144 Palm (0.5) 0,0142 Gypsum bonded particleboard, perpendicular to board 0,0142 WOOD
5 One notch up in complexity: Single objective / Multiple constraints Function One Objective: one performance metric Conflicting Objectives: conflicting performance metrics One Constraint Conflicting Constraints One Constraint Conflicting Constraints Rank by performance metric Rank by most restrictive performance metric Penalty function method Combination of methods The most restrictive constraint determines the performance metric
6 Light car stiff and strong Function: Constraints: underbody panel L and w known must not deform too much must not yield or break Objective: minimal mass Free variables panel thickness t choice of material S F E wt = C1 δ 12L m σ f C 6FL wt 2 = ρ L w t
7 Performance metrics S E wt C1 12L m = ρ L w t σ f C 6FL wt 2 m 1 L 2 12w C 1 2 F δ ρ E m2 6C M1 w L F M 2 ρ σ f M Coupling constant 2 Fδ 6 1 = C' M 2 wl
8 Coupling constant
9 One more notch up in complexity: Conflicting objectives / one constraint Function One Objective: one performance metric Conflicting Objectives: conflicting performance metrics One Constraint Multiple Constraints One Constraint Multiple Constraints Rank by performance metric Rank by most restrictive performance metric Penalty function method Combination of methods The highest penalty function determines the performance metric
40 Conflicting objectives Function: Constraints: underbody panel L and w known must not deform too much Objective: minimal mass minimal thickness Free variables panel thickness t choice of material S F E wt = C1 δ 12L m = ρ L w t
41 Performance metrics m E wt = ρ L w t S C1 12L M 2 m 2 12w L C 1 2 F δ ρ E M1 t 12S C w 1 L 1 E Penalty function Z = α 1 m + α2 t
42 Trade-off surface
4
44 Conflicting objectives Function: Constraints: underbody panel L and w known must not deform too much E at least 5 GPa Objective: minimal mass minimal material cost Free variables panel thickness t choice of material S F E wt = C1 δ 12L m = ρ L w t C = Cm ρ L w t
45 Performance metrics m E wt = ρ L w t S C1 12L C = Cm ρ L w t m : ρ C min m ρ C : min E E Penalty function Z = α m + C
46 CHEAP CAR LIGHT CAR Trade-off surface
47 Exchange constants (Upper bounds to) Exchange constants for mass saving in transport systems Transport System: mass saving Family car (based on fuel saving) Truck (based on payload) Civil aircraft (based on payload) Military aircraft (performance payload) Space vehicle (based on payload) α ( per kg) 0.5 ~ 5 5 to 20 100 to 500 500 to 1000 000 to 10000
48 The ultimate challenge Function One Objective: one performance metric Conflicting Objectives: conflicting performance metrics One Constraint Multiple Constraints One Constraint Multiple Constraints Rank by performance metric Rank by most restrictive performance metric Penalty function method Combination of methods
49 The ultimate Function: Constraints: underbody panel L and w known must not deform too much E at least 5 GPa must not plastically deform or fail must not have brittle failure must resist to water Objective: minimal mass minimal material cost minimal embodied energy Free variables panel thickness t choice of material
50 The objectives minimal mass m = ρ L w t minimal material cost C = Cm ρ L w t minimal embodied energy H = Hm ρ L w t
51 The constraints Screening constraints E at least 5 GPa must resist to water Ranking constraints must not deform too much must not plastically deform or fail must not have brittle failure Ewt S C1 12L 6FL σ f C 2 wt K Ic Yσ πa
52 Material index Objective Constraint Material index Mi Minimum mass Minimum mass Minimum mass Minimum cost Minimum cost Minimum cost Minimum energy Minimum energy Minimum energy Stiffness Strength Toughness Stiffness Strength Toughness Stiffness Strength Toughness ρ E ρ C m m ρ H m ρ H ρ K Ic σ y C ρ m E H m K ρ C m ρ Ic σ y ρ E K Ic σ y
5 Penalty functions Z = i α M i i Z = αi i M M i i,max Stage 1: Index Stage 2: Index Stage : Index Mi/Mmax Mi/Mmax Mi/Mmax SUM Name Polyester/E-glass fiber, pultruded composite rod, unidirectional laminate 0,00171 0,00998 0,00265 1,00 1,00 1,00 20,00 Polyester/45wt% E-glass fiber, woven fabric composite, biaxial laminate 0,00162 0,00601 0,00207 0,95 0,60 0,78 14,87 Polyester/E-glass fiber, non-crimp fabric composite, quasi-isotropic laminate 0,0015 0,00557 0,00185 0,89 0,56 0,70 1,57 Aluminum, 7475, wrought, T651 0,00149 0,0044 0,001 0,87 0,44 0,50 10,74 Aluminum, 7475, wrought, T7651 0,00149 0,00416 0,0016 0,87 0,42 0,51 10,66 Aluminum, 5182, wrought, H19 0,00155 0,0044 0,00126 0,91 0,4 0,48 10,52 Aluminum, 6010, wrought, T6 0,00152 0,00415 0,00125 0,89 0,42 0,47 10,29 Aluminum, 7475, wrought, T761 0,00148 0,00405 0,00122 0,87 0,41 0,46 10,04 max 0,00171 0,00998 0,00265 7 10 weight factor
54 TEXTBOOKS
55 CES EDUPACK 2014 - GrantaDesign http://www.grantadesign.com/education/edupack/edupack2014.htm