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Materials Selection – Case Study 1Bases and Mechanical PropertiesProfessors:Anne Mertens and Davide RuffoniAssistant:Tommaso Maurizi EnriciThursday, October 4, 2018

Mechanical Properties Case Studies Case Study 1: The Lightest STIFF BeamCase Study 2: The Lightest STIFF Tie-RodCase Study 3: The Lightest STIFF PanelCase Study 4: Materials for OarsCase Study 5: Materials for CHEAP and Slender OarsCase Study 6: The Lightest STRONG Tie-RodCase Study 7: The Lightest STRONG BeamCase Study 8: The Lightest STRONG PanelCase Study 9: Materials for ConstructionsCase Study 10: Materials for Small SpringsCase Study 11: Materials for Light SpringsCase Study 12: Materials for Car BodyThursday, October 4, 2018Materials SelectionCES 2009CES 20162

Materials selection Mechanical properties: tensile test, fatigue,hardness, toughness, creep Physical properties: density, conductivity, coefficientof thermal expansion Chemical properties : corrosion Microscopic characteristics: anisotropy ofproperties, hardening, microstructure, grain size,segregation, inclusions Thursday, October 4, 2018Materials Selection3

Materials selection Process linked aspects: formability, machinability,weldability, stampability Aestethic aspects: colour and surface roughnessNotice: surface properties volume ormances4 poles forengineering andmaterial scienceScience ofmaterialsCompositionStructureThursday, October 4, 2018Materials SelectionProperties4

Design stepsMarket NeedDesign toolsFunctionalanalysisMethods forfonctionanalysing3D modelerMaterialsSelectionObjectivesUnderstand thefunctionDefine the maincharacteristicsof the lization(FEM)PrincipleImprovementOptimize shapeOptimizerealisation(manufacturing assembling)DetailingDFM/DFAThursday, October 4, 2018Materials SelectionChoose betweenmain classes ofmaterials(ceramics,metals )Choose betweenfamilies inside amaterial classe(steel, cast iron,Al )Choose aparticularvariety insidethe family (6000or 7000 alloy )ProcessselectionChoose betweenthe main classesof processes(moulding,machining )Choose betweenthe families for agiven processclass (sandcasting, pressurecasting )Choose betweenthe differentvarieties for agiven family ofprocess(moulding, metalmould, Cosworthprocess )5

ForecastsEvolution of materials is challenged by: mechanical properties physical and chemical properties environmental problems (manufacturing) materials ressourceKey Domains : energy (nuclear, solar cells, )transportThursday, October 4, 2018Materials Selection6

A bit of HistoryThursday, October 4, 2018Materials Selection7

A bit of History1850s, time of the Crimean WarNapoleon IIIFrench military engineershad found they couldcontrol the trajectoryapplying a rifling or“spinning” in the barrels ofguns (cannon)The spiraling motion addedextra stressesConsequence?Need a higherstrength material SteelCannon shatterThursday, October 4, 2018Materials Selection8

A bit of History1946, University of PennsylvaniaMoore School of ElectricalEngineering1947,Discovery of the Transistor(Semiconductors)Electronic NumericalIntegrator Analyser andComputer (Eniac) by JohnMauchly and J. PresperEckertThe first general-purposeelectronic computerBuilt from materials such asSilicon and Germanium whichcan either behave as an electricalinsulator or conductorCompanies spent tens ofbillion of dollars to squeezemore circuits on to a small‘chip’ of material17468 thermionic valves70,000 resistors .Covered 167 square metres of floor spaceWeighed 30 tonnesConsumed 160 kW of electricity2010, an Intel X3370 microprocessor – 820 million transistorsYour computer could handle 3 billion instructions /s600000 more than EniacThursday, October 4, 2018Materials Selection9

A bit of History2012, low cost airlinescompanyChange the material of asmall pivot (46)for each seatIn the air transportsWeight CostsAluminum PE Glass fibers CompositeThursday, October 4, 2018Materials Selection10,000,000 dollars saved each year10

Mike Ashby from Univesity of CambridgeThursday, October 4, 2018Materials Selection11

Ashby Diagrams[The mechanical efficiency of natural materials, Mike Ashby, 2003]Thursday, October 4, 2018Materials Selection12

Ashby DiagramsThursday, October 4, 2018Materials Selection13

Ashby DiagramsThursday, October 4, 2018Materials Selection14

Ashby DiagramsThursday, October 4, 2018Materials Selection15

Ashby DiagramsThursday, October 4, 2018Materials Selection16

Ashby DiagramsThursday, October 4, 2018Materials Selection17

Ashby DiagramsThursday, October 4, 2018Materials Selection18

Simplification: Where is the problem?dyhXFor a beam under flexion, the moment of inertia :Length (L): 300 mmThickness (h) 1 mmWidth (b) 25 mmb𝐼𝑌𝑌1 253 1300 𝑚𝑚412In the case of the mechanical properties, it is important toconsider the forces applied, but it is the weakest point thatdetermine the selection.Y25 mmX𝐼𝑋𝑋25 13 2,1 𝑚𝑚412𝐼𝑋𝑋𝑏ℎ3 121 mmIt is possible to change the geometry, but if you cannotWhat can we do?YXThursday, October 4, 2018Materials Selection19

Simplification: Train Wheel (Fast Example)Thursday, October 4, 2018Materials Selection20

The Stiffness designThe Stiffness design is importantto avoid excessive ELASTICdeflectionThursday, October 4, 2018Materials Selection21

The Stiffness designThe Stiffness design is importantto avoid excessive ELASTICdeflectionYour are hereThursday, October 4, 2018Materials Selection22

The StiffnessLFδ𝐹 𝐶1 𝐸𝐼𝑆 3𝛿𝐿𝛿 𝜀 𝐿EI Flexural rigidityI Second Moment of inertiaE Young’s Modulusδ Deflexion10 NC1 3Length (L): 300 mmThickness (h) 1 mmWidth (b) 25 mmProblem :𝐼𝑋𝑋25 13 2,1 𝑚𝑚412𝐼𝑌𝑌1 253 1300 𝑚𝑚412δ?IF we consider that the beam is made of Stainless Steel (E 200 GPa)Which are the consequences if I want to use Polystyrene (E 2 GPa)?IF I can change the thickness and hold the same deflection.Thursday, October 4, 2018Materials Selection23

The StiffnessLF𝐹 𝐶1 𝐸𝐼𝑆 3𝛿𝐿δStainless Steel (E 200 GPa; ρ 7800 kg/m3)Polystyrene (E 2 GPa; ρ 1040 kg/m3)10 NC1 3EI Flexural rigidityI Second Moment of inertiaE Young’s Modulus𝐼𝑌𝑌1 253 1300 𝑚𝑚41210 (0,25)3𝛿 0,02 𝑚𝑚3 200 109 (1300 10 12 )𝐼𝑋𝑋25 13 2,1 𝑚𝑚412𝐹𝐿3𝛿 124 𝑚𝑚𝐶1 𝐸𝑌𝑋𝑋𝑊𝑖𝑡ℎ 𝛿 124 𝑚𝑚12𝐼𝑋𝑋ℎ 𝑤1/3𝐼𝑋𝑋10 (0,25)34 210𝑚𝑚3 2 109 (0,124)12 210 25Thursday, October 4, 20181/3 4,6 𝑚𝑚SteelPS𝑊ℎ𝑒𝑛 ℎ(𝑆𝑡𝑒𝑒𝑙) 1 𝑚𝑚Materials Selection24

The StiffnessLFδ10 NC1 3𝐹 𝐶1 𝐸𝐼𝑆 3𝛿𝐿Length: 300 mmWidth 25 mmStainless Steel (E 200 GPa; ρ 7800 kg/m3)Polystyrene (E 2 GPa; ρ 1040 kg/m3)About the weight?EI Flexural rigidityI Second Moment of inertiaE Young’s Modulusδ DeflexionThickness 1 mmThickness 4,6 mm𝑚𝑆𝑆 7800 0,3 0,025 0,001 59 𝑔𝑟𝑚𝑃𝑆 1040 0,3 0,025 0,046 36 𝑔𝑟BIGGER SectionBUT LIGHTERDepends on what you need and the conditionsThursday, October 4, 2018Materials Selection25

The Materials Selection approachCase Study 1:Find the Lightest STIFF BeamObjective Minimize the massConstraints Stiffness specified Length L Square shapeLFFree Variables Area (A) of the cross-section Choice of the materialδEI Flexural rigidityI Second Moment of inertiaE Young’s Modulusδ DeflexionLength: 300 mmC1 3Hypothesis:𝐹 𝛿 𝑆 𝑆𝑚𝑖𝑛100 N𝐹𝐶1 𝐸𝐼 𝑆𝑚𝑖𝑛 3𝛿𝐿𝑚 𝐴 𝐿 𝜌Thursday, October 4, 2018Materials Selection𝐴 𝑚𝐿 𝜌m massA area of the sectionL Lengthρ Density26

The Materials Selection approachCase Study 1:Find the Lightest STIFF BeamBeam: Square Sectionb hLdyFhδXY𝐴 𝑚𝐿 𝜌12 𝑆𝑚 𝐶1 𝐿Thursday, October 4, 2018Since A b2𝑏ℎ3 𝐴2𝐼 1212100 NC1 3𝐹 𝐶1 𝐸𝐼 3 𝑆𝑚𝑖𝑛𝛿𝐿𝑚𝐴 𝐿 𝜌bThe Area will be the Free Variable1/2 𝐿3 𝜌𝐸1/2𝑚Materials Selection𝐸1/2𝜌Just remember:Constraints StiffnessspecifiedLength LSquare shape27

The Material Index (M)Case Study 1:Find the Lightest STIFF BeamM For instance𝐴𝐵Log(M) 𝐿𝑜𝑔 𝐴 𝐿𝑜𝑔(𝐵)Log(A) 𝐿𝑜𝑔(𝐵) 𝐿𝑜𝑔 𝑀𝐸 1/2𝜌A1Slope1Selection Direction ( )BThursday, October 4, 2018Materials Selection28

Ashby DiagramsThursday, October 4, 2018Materials Selection29

The Material Index (M)Case Study 1:Find the Lightest STIFF Beam𝑚𝐸1/2𝜌2Slope1Stainless Steel(E 200 GPa; ρ 7800 kg/m3)Polystyrene(E 2 GPa; ρ 1040 kg/m3)Thursday, October 4, 2018Materials Selection30

Lightest Beam (Bending conditions)Case Study 1:Find the Lightest STIFF BeamWidth 25 mmF 100 Nδ 0,34 mmSmin 296 103 N/m12 𝑆𝑚 𝐶1 𝐿𝑚𝐴 𝐿 𝜌Thursday, October 4, 2018 Width and thickness?Stainless Steel (E 200 GPa; ρ 7800 kg/m3)Polystyrene (E 2 GPa; ρ 1040 kg/m3)1/2𝐿3Length: 300 mmThickness 1 mm MaterialWeight (kg)A (mm2)Width e1,25400063𝜌𝐸1/2Materials Selection31

CESCase Study 1:Find the Lightest STIFF BeamTo Minimize mass2Slope1Thursday, October 4, 2018Materials Selection32

To Minimize StiffnessCES2Slope1Depends on what you need It is not in flexionThursday, October 4, 2018Materials Selection33

Ok, slow down.Case Study 2:Find the Lightest STIFF Tie-RodTie-Rod TRACTION CONDITIONSDATAF 1000 NDimensions:Length: 300 mmThickness 1 mmWidth 25 mmObjective Minimize the massConstraints Stiffness specified Length LFree Variables Area (A) of the cross-section Choice of the materialIn Traction,the shape of the cross-section is not important𝑚𝑚 𝐴 𝐿 𝜌𝐴 𝐿 𝜌𝜎𝐹𝑟𝑜𝑚 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝐸𝜀𝐹 𝑆𝑚𝑖𝑛 𝑆𝐹𝑟𝑜𝑚 𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛: 𝛿 𝜀 𝐿𝛿𝐹 𝜎 𝐴Thursday, October 4, 2018Materials Selection34

Lightest Tie-Rod (Traction conditions)Case Study 2:Find the Lightest STIFF Tie-RodF 1000 Nδ 3,78 10 3 mmSmin 264,5 106 N/mDimensions:Length: 300 mmThickness 1 mmWidth 25 mm𝐹 𝑆𝑚𝑖𝑛 𝑆𝛿𝜎 𝐴 𝑆𝑚𝑖𝑛𝜀 𝐿𝑚 𝑆 𝑚𝐴 𝐿 𝜌𝑚 (264,5 106 ) (300 10 3 )2 𝜌𝐸𝜌 𝐸Thursday, October 4, 2018𝐸 𝐴 𝑆𝑚𝑖𝑛𝐿Materials Selection𝑚𝐿2𝜌 𝐸𝐸𝜌35

CES𝑚Case Study 2:Find the Lightest STIFF Tie-RodThursday, October 4, 2018Materials Selection𝐸𝜌36

Lightest Tie-Rod (Traction conditions)Case Study 2:Find the Lightest STIFF Tie-RodF 1000 Nδ 3,78 10 3 mmSmin 264,5 106 N/mDimensions:Length: 300 mmThickness 1 mmWidth 25 mmThursday, October 4, 2018𝐸 𝐴 𝑆𝑚𝑖𝑛𝐿𝑚𝐴 𝐿 𝜌𝑚 𝑆 𝐿2𝜌 𝐸𝑚𝐸𝜌Stainless Steel (E 200 GPa; ρ 7800 kg/m3)Silicon carbide (E 430 GPa; ρ 3150 kg/m3)Al Alloys (E 75 Gpa; ρ 2700 kg/m3)MaterialWeight (kg)A (mm2)Width andThickness(mm)SiliconCarbide0,174179,813,4Al Alloys0,856105032,4Materials Selection37

Change of the sectionPanel:b fixedh freeBeam: SquareSectionb hPanel:h fixedb freeThursday, October 4, 2018Materials Selection38

Lightest Panel (Bending conditions)Case Study 3:Find the Lightest STIFF PanelLδC1 3ZHypothesis:𝐹 𝛿 𝑆 𝑆𝑚𝑖𝑛Length: 300 mmWidth: 25 mmThursday, October 4, 2018 Minimize the massConstraints Stiffness specified Length L and b specifiedFree Variables h (thickness) of the cross-section Choice of the materialFYObjective100 NhYb 25 mmX𝐹 𝐶1 𝐸𝐼 3 𝑆𝑚𝑖𝑛𝛿𝐿𝑚 𝐴 𝐿 𝜌Materials Selection𝐴 𝑚𝐿 𝜌m massA area of the sectionL Lengthρ Density39

Lightest Panel (Bending conditions)Case Study 3:Find the Lightest STIFF PanelPanel:Since A bhb fixedh free𝐴𝑏 𝑏𝐼 12𝐴ℎ 𝑏3𝐴3 12 𝑏2𝐶1 𝐸𝐼𝐿3𝑚𝐴 𝐿 𝜌𝑆𝑚𝑖𝑛 hYb 25 mmX𝑚𝐴 𝐿 𝜌The Area will be the Free Variable, but all theconsequences of the selection are on the thickness12 𝑆 𝑏2𝑚 𝐶1Thursday, October 4, 20181/3 𝐿2 𝜌𝐸1/3𝑚Materials Selection𝐴ℎ 𝑏𝐸1/3𝜌40

CESCase Study 3:Find the Lightest STIFF PanelThursday, October 4, 2018𝑚Materials Selection𝐸1/3𝜌41

Bending conditions𝑚𝑚𝐸1/2𝜌𝐸1/3𝜌Stainless Steel(E 200 GPa; ρ 7800 kg/m3)Polystyrene(E 2 GPa; ρ 1040 kg/m3)Thursday, October 4, 2018Materials Selection42

Bending conditionsF 100 Nδ 0,34 mmSmin 296 103 N/mBeamPanel (b 25 mm)Thursday, October 4, 2018Stainless Steel (E 200 GPa; ρ 7800 kg/m3)Polystyrene (E 2 GPa; ρ 1040 kg/m3)MaterialWeight (kg)A (mm2)Thicknessh aterials Selection43

Stiffness �𝑖𝑛𝛿𝑚𝑎𝑥Stiffness – Traction :Thursday, October 4, 2018Stiffness – Bending :Materials Selection𝐴𝑡 𝑓𝑖𝑥𝑒𝑑 𝑆𝑚𝑖𝑛𝐴𝑡 𝑓𝑖𝑥𝑒𝑑 𝑚Stiffness – Bending :44

Case Study 4:Materials for OarsThursday, October 4, 2018Materials Selection45

Case Study 4:Materials for OarsObjective Minimize the massConstraints Stiffness specified Length L Circular shape (beam)Free Variables Area (A) of the cross-section Choice of the materialL (Outboard) 2 mThursday, October 4, 2018Materials Selection46

Case Study 4:Materials for Light OarsWe assume solid section𝐴 π 𝑟2𝜋𝑟 4 𝐴2𝐼 44𝜋𝑟YZYX𝐹𝐶1 𝐸𝐼 𝑆𝑚𝑖𝑛 3𝛿𝐿𝑚𝐴 𝐿 𝜌𝐴 𝑚𝐿 𝜌4 𝜋 𝑆 𝐿5𝑚 3𝑚Thursday, October 4, 2018Materials Selection1/2 𝜌𝐸1/2𝐸1/2𝜌47

𝑚Case Study 4:Materials for Light OarsThursday, October 4, 2018Materials Selection𝐸1/2𝜌48

Case Study 4:Materials for Light and Slender OarsWe assume solid section𝐴 π 𝑟2𝜋𝑟 4 𝐴2𝐼 44𝜋Y𝑟ZYX𝐹𝐶1 𝐸𝐼 𝑆𝑚𝑖𝑛 3𝛿𝐿𝜋𝑟 4 𝐴2𝐼 44𝜋4 𝜋 𝑆 𝐿3𝐴 3Place LIMITS to a single PropertyEvaluating the Properties ChartThursday, October 4, 20181/2 1𝐸1/2𝐴𝐸10 Gpa E 200 GPaMaterials Selection49

Case Study 4:Materials for Light andOarsSlender OarsCFRP - best material with more control of the propertiesBamboo – Traditional material for oars for canoesWoods – Traditional, but with natural variabilitiesCeramics – Low toughness and high costThursday, October 4, 2018Materials Selection𝑚𝐸1/2𝜌10 Gpa E 200 GPa50

Case Study 4:Materials for Light andOarsSlender Oars𝜋𝑟 4 𝐴2𝑆𝑜𝑙𝑖𝑑 𝐼 44𝜋𝑇𝑢𝑏𝑒 𝐼 𝜋𝑟 3 𝑡3 𝑚2 𝐸𝑆 4 𝜋 𝐿5 𝜌2𝑚𝐴𝑡 𝑓𝑖𝑥𝑒𝑑 𝑆𝑚𝑖𝑛1,58 kgProbably Tube shapeAssume 2,5 kg for a Solid Oar (exagerated)CFRP (E 110 GPa; ρ 1550 kg/m3)Bamboo (E 17,5 GPa; ρ 700 kg/m3)SCFRP 853,94 N/mSBamboo 666,1 N/m𝑆𝑚𝑖𝑛𝛿𝑚𝑎𝑥𝐴𝑡 𝑓𝑖𝑥𝑒𝑑 𝑚Thursday, October 4, 2018CFRP good for Competition OarMaterials Selection51

Case Study 5:Materials for CHEAP and Slender OarsObjective Minimize the costConstraints Stiffness specified Length L Circular shape (beam)FreeVariables Area (A) of the cross-section Choice of the materialL (Outboard) 2 mThursday, October 4, 2018Materials Selection52

Case Study 5:Materials for CHEAP and Slender Oars4 𝜋 𝑆 𝐿5𝑚 31/2 𝜌𝐸1/2𝐶 𝑚 𝐶𝑚𝑚 𝐶𝐶𝑚𝑪 Cost𝑪𝒎 Cost per unit of mass4 𝜋 𝑆 𝐿5𝐶 3𝐶1/2𝜌 𝐶𝑚 1/2𝐸𝐸1/2𝜌 𝐶𝑚Better to consider cost alwaysas a function of massThursday, October 4, 2018Materials Selection53

Case Study 5:Materials for CHEAP and Slender Oars𝐶𝐸1/2𝜌 𝐶𝑚Bamboo – Traditional material for oars for canoes10 Gpa E 200 GPaWoods – Traditional, but with natural variabilitiesStone and Concrete – Low toughness and difficult to manufactureThursday, October 4, 2018Materials Selection54

Case Study 5:Materials for CHEAP and Slender Oars4 𝜋 𝑆 𝐿5𝑚 31/2 𝜌4 𝜋 𝑆 𝐿5𝐶 3𝐸1/2𝐶 𝑚 𝐶𝑚1/2𝜌 𝐶𝑚 1/2𝐸𝐶𝑚 𝐶𝑚𝑪 Cost𝑪𝒎 Cost per unit of mass𝐶𝐸1/2𝜌 𝐶𝑚Better to consider cost alwaysas a function of massWoods good for Commercial OarThursday, October 4, 2018Materials Selection55

The Strength designThe Strength design is importantto avoid plastic collapse or maybe notThursday, October 4, 2018Materials Selection56

The Strength designThe Strength design is importantto avoid plastic collapseYour are hereThursday, October 4, 2018Materials Selection57

Lightest Tie-Rod (Traction conditions)Case Study 6:Find the Lightest STRONG Tie-RodObjective Minimize the massConstraints Support tensile load Fwithout yielding Length LFreeVariables Area (A) of the crosssection Choice of the materialFLDATAF 1000 NDimensions:Length: 300 mmThickness 1 mmWidth 25 mmIn Traction,the shape of the cross-section is not important𝑚𝑚 𝐴 𝐿 𝜌𝐴 𝐿 𝜌𝐹𝐹𝑟𝑜𝑚 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝜎𝑦𝐴Thursday, October 4, 2018Materials Selection𝑚 𝐹 𝐿 𝜌𝜎𝑦58

Ashby DiagramsThursday, October 4, 2018Materials Selection59

CESCase Study 6:Find the Lightest STRONG Tie-RodThursday, October 4, 2018𝑚Materials Selection𝜎𝑦𝜌60

Lightest Tie-Rod (Traction conditions)Case Study 6:Find the Lightest STRONG Tie-Rod𝑚 𝐹 𝐿 𝑚𝜌𝜎𝑦𝜎𝑦𝜌It is possible to do as before, but let’s calculate the maximum Fon the precedent Tie-RodMaterialWeight (kg)Width andThickness(mm)Al Alloys1,25630 kNElastic ThroughoutThursday, October 4, 2018𝐹 Stainless Steel (𝜎𝑦 600 MPa; ρ 7800 kg/m3)Wood (𝜎𝑦 50 MPa; ρ 700 kg/m3)Al Alloys (𝜎𝑦 270 Mpa; ρ 75 kg/m3)𝑚 𝜎𝑦 416 𝑘𝑁𝐿 𝜌X kNPlastic deformation/ CollapseMaterials Selection61

Lightest Beam (Bending conditions)Case Study 7:Find the Lightest STRONG BeamObjective Minimize the massConstraints Stiffness specified Length L Square shapeLMfC1 3Length: 300 mmHypothesis: ymax h/2 𝜎𝑚𝑎𝑥 𝜎100 N𝜎𝑚𝑎𝑥Free Variables Area (A) of the cross-section Choice of the materialM Momentσ Stressymax max distance from theneutral axis 𝜎𝑚𝑎𝑥Thursday, October 4, 2018𝐴 b hSince A b2𝑏ℎ3𝐴3/2𝐼 126𝑀𝑓 𝑦𝑚𝑎𝑥 𝜎𝑓𝐼𝑚 𝐴 𝐿 𝜌Beam: Square Section𝑚𝐿 𝜌Materials Selection62

Lightest Beam (Bending conditions)Case Study 7:Find the Lightest STRONG Beam23/2𝑏ℎ𝐴𝐼′ 66ℎ𝑀𝑓 2𝑀𝑓 𝑦𝑚𝑎𝑥𝑀𝑓 𝜎𝑓𝑏ℎ3𝐼𝐼′12𝑚𝑚 𝐴 𝐿 𝜌𝐴 𝐿 𝜌𝜎𝑚𝑎𝑥 𝑀𝑓 6 𝑀𝑓 6 𝐿3/2 𝜌3/2𝜎𝑓 3/2 𝐴𝑚3/2𝑚 (𝑀𝑓 6)2/3 L 𝑚Thursday, October 4, 2018Materials Selection𝜌𝜎𝑓 2/3𝜎𝑦 2/3𝜌63

CESCase Study 7:Find the Lightest STRONG BeamThursday, October 4, 2018𝑚Materials Selection𝜎𝑦 2/3𝜌64

Lightest Beam (Bending conditions)Case Study 7:Find the Lightest STRONG Beam𝑏ℎ2 𝐴3/2𝐼′ 66ℎ𝑀𝑓 2𝑀𝑓 𝑦𝑚𝑎𝑥𝑀𝑓 𝜎𝑓𝑏ℎ3𝐼𝐼′12𝑚𝑚 𝐴 𝐿 𝜌𝐴 𝐿 𝜌𝜎𝑚𝑎𝑥 𝑀𝑓 6 𝑀𝑓 6 𝐿3/2 𝜌3/2𝜎𝑓 3/2 𝐴𝑚3/2𝑚 (𝑀𝑓 6)2/3 L It is always better to choose ashape that uses less materialto provide the same strengthTO SUPPORT BENDINGThursday, October 4, 2018𝑚Materials Selection𝜌𝜎𝑓 2/3𝜎𝑦 2/3𝜌65

Lightest Panel (Bending conditions)Case Study 8:Find the Lightest STRONG PanelLC1 3Length: 300 mmHypothesis: ymax h/2 𝜎𝑚𝑎𝑥 𝜎Constraints Stiffness specified Length L and b specifiedhYb 25 mmX𝜎𝑚𝑎𝑥𝑀𝑓 𝑦𝑚𝑎𝑥 𝜎𝑓𝐼𝑚 𝐴 𝐿 𝜌Thursday, October 4, 2018 Minimize the massFree Variables h (thickness) of the cross-section Choice of the materialMf100 NObjective𝐴 𝐼′ 𝑚𝐿 𝜌Materials Selection𝑏ℎ26 𝐴2𝑏 6Since A bhℎ 𝐴𝑏66

Lightest Panel (Bending conditions)Case Study 8:Find the Lightest STRONG Panel𝜎𝑚𝑎𝑥𝑏ℎ2𝐴2𝐼′ 6𝑏 6𝑀𝑓 𝑦𝑚𝑎𝑥 𝑀𝑓 𝑏 6 𝑀𝑓 𝜎𝑓𝐼𝐴2𝐼′𝑚 𝐴 𝐿 𝜌𝑀𝑓 𝑏 6 𝑀𝑓 6 𝑏 𝐿2 𝜌2𝜎𝑓 𝐴2𝑚2𝑚𝐴 𝐿 𝜌𝑚 (𝑀𝑓 6 𝑏)1/2 L 𝑚Thursday, October 4, 2018Materials Selection𝜌𝜎𝑓 1/2𝜎𝑦 1/2𝜌67

CESCase Study 8:Find the Lightest STRONG PanelThursday, October 4, 2018𝑚Materials Selection𝜎𝑦 1/2𝜌68

Lightest Panel (Bending conditions)Case Study 8:Find the Lightest STRONG Panel𝑏ℎ2 𝐴3/2𝐼′ 66ℎ𝑀𝑓 2𝑀𝑓 𝑦𝑚𝑎𝑥𝑀𝑓 𝜎𝑓𝑏ℎ3𝐼𝐼′12𝑚𝑚 𝐴 𝐿 𝜌𝐴 𝐿 𝜌𝜎𝑚𝑎𝑥 𝑀𝑓 6 𝑀𝑓 6 𝐿3/2 𝜌3/2𝜎𝑓 3/2 𝐴𝑚3/2𝑚 (𝑀𝑓 6 𝑏)1/2 L It is always better to choose ashape that uses less materialto provide the same strengthTO SUPPORT BENDINGThursday, October 4, 2018𝑚Materials Selection𝜌𝜎𝑓 1/2𝜎𝑦 1/2𝜌69

Summary (to minimize the mass)Stiffness – Traction :Strength – Traction :Stiffness – Bending ���𝑦 2/3𝜌𝜎𝑦 1/2𝜌Stiffness – Bending (Panel):Strength – Bending (Panel):Strength – Bending :Thursday, October 4, 2018Materials Selection70

Case Study 9:Materials for ConstructionsThursday, October 4, 2018Some data : Nowadays, half the expense of building ahouse is the cost of the materialsFamily house : 200 tonsLarge apartment block : 20,000 tonsMaterials Selection71

Mr. Pincopallo asksa new coverCase Study 9:Materials for ConstructionsUnderstand the problem andtranslate it in selection criteria,thus properties,A cover has 3 BROAD ROLES:Cladding: Protection from theenvironmentThe frames: Mechanical supportInternal surfacing: Control heat,light and soundThursday, October 4, 2018Materials Selection72

Case Study 9:Materials for Constructions(Structural Frame)Objective Minimize the costConstraints Length L specified Stiffness: must not deflect toomuch under loads Strength: must not fall underdesign loadsFree Variables Area (A) of the cross-section Choice of the materialHypothesis:𝐹 𝛿 𝑆𝑚𝑖𝑛 𝑆Floor joints are beams, loaded in bending.4 𝜋 𝑆 𝐿5𝐶 3𝐹𝐶1 𝐸𝐼 𝑆𝑚𝑖𝑛 3𝛿𝐿𝑚 𝐴 𝐿 𝜌𝐶 𝑚 𝐶𝑚Thursday, October 4, 2018𝑚𝐿 𝜌𝐶𝑚 𝐶𝑚1/2𝜌 𝐶𝑚 1/2𝐸𝐴 Materials Selection𝐶𝐸1/2𝜌 𝐶𝑚73

Case Study 9:Materials for Constructions(Structural Frame)Objective Minimize the costConstraints Length L specified Stiffness: must not deflect toomuch under loads Strength: must not fall underdesign loadsFree Variables Area (A) of the cross-section Choice of the material𝑏ℎ3 𝐴3/2𝐼 126𝜎𝑚𝑎𝑥Floor joints are beams, loaded in bending.𝑀𝑓 𝑦𝑚𝑎𝑥 𝜎𝑓𝐼𝑚 𝐴 𝐿 𝜌𝐶 𝑚 𝐶𝑚Thursday, October 4, 2018𝐶 (𝑀𝑓 𝑚𝐿 𝜌𝐶𝑚 𝐶𝑚6)2/3𝜌 𝐶𝑚 L 2/3𝜎𝑓𝐴 Materials Selection𝐶𝜎𝑓 2/3𝜌 𝐶𝑚74

Case Study 9:Materials for ConstructionsATTENTION!!!Selection with the cost/kg andwith the cost/m3 isDIFFERENTThursday, October 4, 2018Materials Selection75

𝐶Case Study 9:Materials for ConstructionsThursday, October 4, 2018Materials Selection𝐸1/2𝜌 𝐶𝑚76

𝐶Case Study 9:Materials for ConstructionsThursday, October 4, 2018Materials Selection𝜎𝑓 2/3𝜌 𝐶𝑚77

Case Study :Materials for SpringsThursday, October 4, 2018Materials Selection78

Case Study 10:Materials for Small SpringsObjective Maximize stored elastic energyConstraints No failure σ 𝜎𝑓 throughoutthe springFree Variables Choice of the material𝐶𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦𝜎𝑦 𝜎𝜎 𝐸 𝜀𝜎𝜀 𝐸𝑆𝑀𝐴𝐿𝐿? ? 𝑽 FREE VARIABLE!!dV dxdydz[Solid Mechanics Part I Kelly]Thursday, October 4, 2018Materials Selection79

Case Study 10:Materials for Small Springs𝜎𝑦 𝜎Strain energy density𝜎𝜀 𝐸dV dxdydz𝑚 𝑉 𝜌11𝑊𝑒𝑙 න 𝜎 𝜀 𝑑𝑉 𝜎 𝜀 𝑉22Total strain energy in the piece considered𝜎𝑦 2𝑊𝑒𝑙 𝑀12𝐸Total strain energyPER UNIT OF VOLUME[Solid Mechanics Part I Kelly]Thursday, October 4, 2018Materials Selection80

Case Study 10:Materials for Small Springs Thursday, October 4, 2018 CFRP Comparable in performance with steel; expensive[TRUCK SPRINGS]STEEL The traditional choice: easily formed and heat treatedTITANIUM Expensive, corrosion resistantRUBBERS have Excellent M1but low tensile strength high lossfactorNYLON Inexpensive and easilyshaped, but high loss factor[CHILDREN’S TOYS]Materials Selection81

Case StudyMaterials for Springs𝜎𝑦 2𝑊𝑒𝑙 2𝐸Valid for axial springsBecause much of the material is notfully loadedPAY ATTENTION𝜎𝑦 2𝑊𝑒𝑙 3𝐸For torsion springs (less efficient)Thursday, October 4, 2018Materials Selection82

Case StudyMaterials for Springs𝜎𝑦 2𝑊𝑒𝑙 4𝐸For leaf springs (less efficient)Thursday, October 4, 2018Materials Selection83

Case Study 9:Materials for Light Springs𝜎𝑦 𝜎Strain energy density𝜎𝜀 𝐸dV dxdydz𝑽𝐿𝐼𝐺𝐻𝑇? ? 𝝆 FREE VARIABLE!!𝑚 𝑉 𝜌11𝑊𝑒𝑙 න 𝜎 𝜀 𝑑𝑉 𝜎 𝜀 𝑉22Total strain energy in the piece considered𝜎𝑓 2𝑊𝑒𝑙 𝑀2𝜌2 𝐸 𝜌Total strain energyPER UNIT OF MASS[Solid Mechanics Part I Kelly]Thursday, October 4, 2018Materials Selection84

Case Study 11:Materials for Light Springs CFRP Comparable in performance with steel; expensive[TRUCK SPRINGS]RUBBERS 20 times better than Steel; but low tensile strengthhigh loss factorNYLON Inexpensive and easily shaped, but high loss factor[CHILDREN’S TOYS]METALS AlmostDISAPPEAREDThursday, October 4, 2018Materials Selection85

Case Study 12:Materials for Car Body𝑆𝑜𝑚𝑒 𝑐𝑜𝑛𝑡𝑒𝑥𝑡 Car Evolution1932 Ford Model B1934 Bonnie and Clyde carThursday, October 4, 2018Materials Selection86

Case Study 12:Materials for Car Body𝑆𝑜𝑚𝑒 𝑐𝑜𝑛𝑡𝑒𝑥𝑡 Car Evolution1932 Ford Model B1970 Buick GSXKm/h2010 Ferrari 458 Italia325 km/h184 km/h80 km/hThursday, October 4, 2018Materials Selection87

Case Study 12:Materials for Car Body𝐷𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛? ? 𝐸𝑁𝐸𝑅𝐺𝑌 𝐶𝑂𝑁𝑆𝑈𝑀𝑃𝑇𝐼𝑂𝑁At first, automotive industrymove to too deformable carsand then move to have a mixFOR PEOPLE SAFETYSometimes exaggerateThursday, October 4, 2018Materials Selection88

Case Study 12:Materials for Car Body(Car Hood or Car Door)Objective Maximize plastic deformation at highloadConstraints Free VariablesGeometry𝐻𝑖𝑔ℎ 𝜎𝑦Division for priceConsider manufacture Choice of the material𝐿𝐼𝐺𝐻𝑇? ? 𝑚𝜎𝑓 2𝑊𝑒𝑙 𝑀2𝜌2 𝐸 𝜌Total strain energyPER UNIT OF MASSThursday, October 4, 2018Materials Selection89

Case Study 12:Materials for Car Body(Car Hood or Car Door)Objective Maximize plastic deformation at highloadConstraints 𝐿𝐼𝐺𝐻𝑇? ? 𝑚𝜎𝑓 2𝑊𝑒𝑙 𝑀2𝜌2 𝐸 𝜌Total strain energyPER UNIT OF MASSFree VariablesGeometry𝐻𝑖𝑔ℎ 𝜎𝑦Division for priceConsider manufacture Choice of the materialSteps: Stiffness selection (Take off flexible materials)Yield strength selection to minimize the costs (Automotive)Minimum Yield StrengthMaximization of stored energyThursday, October 4, 2018Materials Selection90

Case Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018𝑚Materials Selection𝐸𝜌91

Case Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018Materials Selection92

Case Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝜎𝑦 (200 MPa)Materials Selection93

𝜎𝑓 2𝑊𝑒𝑙 𝑀12𝐸Total strain energyPER UNIT OF VOLUMECase Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018Materials Selection94

𝜎𝑓 2𝑊𝑒𝑙 𝑀2𝜌2 𝐸 𝜌Total strain energyPER UNIT OF MASSCase Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018Materials Selection95

𝜎𝑓 2𝑊𝑒𝑙 𝑀2𝜌2 𝐸 𝜌Total strain energyPER UNIT OF MASSCase Study 12:Materials for Car Body(Car Hood or Car Door)Lamborghini Huracan 2015Thursday, October 4, 2018Materials Selection96

Case Study 12:Materials for Car Body(Car Hood or Car Door)Manufacturing day, October 4, 2018Materials Selection97

Case Study 12:Materials for Car Body(Car Hood or Car Door)Vacuum and pressurebag moldingNot adapt for high productionsNo way for acommercial carThursday, October 4, 2018Materials Selection98

Case Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018And which Metal?Materials Selection𝜎𝑓 2𝑊𝑒𝑙 𝑀2𝜌2 𝐸 𝜌Total strain energyPER UNIT OF MASS99

Case Study 12:Materials for Car Body(Car Hood or Car Door)StampingAdapt for high productionsThursday, October 4, 2018Materials Selection100

PROCESSABILITYCase Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018Metals easy to stampMaterials Selection101

Case Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018𝜎𝑓 2𝑊𝑒𝑙 𝑀2𝜌2 𝐸 𝜌Total strain energyPER UNIT OF MASSMaterials Selection Minimum Formability (4)102

PROCESSABILITYCase Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018Metals easy to stampMaterials Selection103

Case Study 12:Materials for Car Body(Car Hood or Car Door)Thursday, October 4, 2018𝜎𝑓 2𝑊𝑒𝑙 𝑀2𝜌2 𝐸 𝜌Total strain energyPER UNIT OF MASSMaterials Selection Minimum Formability (4) Minimum Brazability (3)104

Case Study 12:Materials for Car Body(Car Hood or Car Door)BMW M3 – Low alloy steelAudi A8 – Al-alloysDeeper selection?LEVEL l-vs-aluminum-lightweight-wars-heat]Thursday, October 4, 2018Materials Selection105

Materials Selection StepsOptional:Thursday, October 4, 2018Materials Selection106

Thursday, October 4, 2018 Materials Selection 2 Mechanical Properties Case Studies Case Study 1: The Lightest STIFF Beam Case Study 2: The Lightest STIFF Tie-Rod Case Study 3: The Lightest STIFF Panel Case Study 4: Materials for Oars Case Study 5: Materials for CHEAP and Slender Oars Case Study 6: The Lightest STRONG Tie-Rod Case Study 7: The Lightest STRONG Beam

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