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## IFB 2012 Materials Selection in Mechanical Design

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**Shape of cross section is kept constant. Only the material**changes. IFB 2012Materials Selection in Mechanical Design INTRODUCTIONMaterials Selection Without Shape (1/2)Textbook Chapters 5 & 6 IFB 2012 INTRODUCTION Material Indices**Minimise mass, m:**Goal Constraint Stiffness of the beam, S: I = second moment of area: Material Index { What can be varied ? • Material choice • Area = b2 Chose materials with largest M= Deriving Materials Indices, Example 1: Material for a stiff, light beam Function Beam (solid square section) m = mass A = cross section L = length = density b = edge length S = stiffness I = second moment of area E = Young’s modulus Get these equations from the textbook, or pdf file “Useful Solutions” b2 = m/L b4 = 12 SL3/CE b2 = Free variable (Trade-off variable) IFB 2012 INTRODUCTION Material Indices Maximise Material Index ! To minimise the mass**Elastic Bending of Beams and Panels; p. 533 or from pdf**file “useful solutions” IFB 2012 INTRODUCTION Material Indices**Moments of Sections; p 531, or file “Useful Solutions”**IFB 2012 INTRODUCTION Material Indices**Material Index**{ What can be varied ? • Material choice. • Panel thickness t Chose materials with largest M= Deriving Materials Indices, Example 2: Material for a stiff, light panel Function Panel, width w and length Lspecified Goal Minimise mass, m Constraint Stiffness of the panel, S m = mass w = width L = length = density t = thickness S = stiffness I = second moment of area E = Young’s modulus Free variable..?? Eliminatet IFB 2012 INTRODUCTION Material Indices**Objective: minimisemass**Material Indices for Minimum Mass Function Index Same Volume Tension (tie) Bending (beam) Bending (panel) Objective: minimise mass for given stiffness To minimise the mass Maximise Material Index ! IFB 2012 INTRODUCTION Material Indices**Materials Selection using charts: effect of slope of**selection line Exam question: What is the Physics behind the different exponents in the Indices’ equations? Index Different materials are selected, depending on the slope of the selection line Selection line slope 1 Selection line slope 2 Selection line slope 3 MECH4301 2011 Lecture 2 Charts**This is how the world looks like after you pass the**Materials Selection Course Demystifying Material Indices IFB 2012 INTRODUCTION Material Indices**Material 1, Mass 1 stiffness S**Materials 2, Mass 2 stiffness S Demystifying Material Indices (beam, elastic bending) For given shape, the reduction in mass at constant bending stiffness is given by the reciprocal of the ratio of material indices. Same applies to bending strength. IFB 2012 INTRODUCTION Material Indices**heavier**lighter Example: How good are Mg and Al when it comes to reducing mass? A 10 kg component made of Steel… m2/m1 = M1/M2 Exam question: Which beam is fatter?? Same: Which panel is thicker?? IFB 2012 INTRODUCTION Material Indices**Comparative weight of panels of equal stiffness (Steel, Ti,**Al and Mg) (Emley, Principles of Mg Technology) The Mg-Li panel is thicker IFB 2012 INTRODUCTION Material Indices**Example of solution to Tutorial # 1 (Exercise 7.3)**IFB 2012 INTRODUCTION Material Indices**Example of solution to Tutorial # 1 (Exercise 7.3)**Derivation of the Material Index: When fully loaded,the beam should not fail, i.e., maximum < * (yield strength) m = lASolve for A= m/l. The maximum force is I/ym=A3/2/6 Solving for m: Material Index : M = (*)2/3/. Select using the - chart with a line of slope 1.5, on the upper left corner. 2011 Lecture 3 Material Indices**Select using the - chart with a line of slope 1.5,**upper left corner. Copy the results from CES Sort the materials by their Index Conclusions to the chart/table: Composites, timber are the best materials. Al, Mg and steels are good competitors. Foams perform generally well, due to their low density. However, if made out of foams, the beams will be rather fat/big! 2011 Lecture 3 Material Indices**The End Introduction**IFB 2012 INTRODUCTION Material Indices**The CES software: Demonstration**IFB 2012 INTRODUCTION Material Indices**Member**Class Attributes Kingdom Family Density Mechanical props. Thermal props. Electrical props. Optical props. Corrosion props. Supporting information -- specific -- general • Ceramics • & glasses • Metals • & alloys • Polymers • & elastomers • Hybrids Steels Cu-alloys Al-alloys Ti-alloys Ni-alloys Zn-alloys 1000 2000 3000 4000 5000 6000 7000 8000 Materials A material record Organising information: the MATERIALS TREE IFB 2012 INTRODUCTION Material Indices**CES : the 3 levels**3400 Level 2 enough for most exercises IFB 2012 INTRODUCTION Material Indices**E**density Chart created with the CES software (level 1, 60 materials) IFB 2012 INTRODUCTION Material Indices**E**density Chart created with the CES software (level 3, ~3400 materials) IFB 2012 INTRODUCTION Material Indices**Selection corner**E 1 Selection line for tie rods Selection line for beams Selection line for panels 2 3 Ranking Materials using Charts ceramics metals composites & polymers One very significant conclusion from this course, so far: For beams and panels, materials with very low density are more important than for tie-rods. This is why foams are not used for tie rods, but are preferred for beams and more so for flat panels. foams Important: Read textbook pp.93-95: Summary and Conclusions to Ch. 4, Properties of charts. IFB 2012 INTRODUCTION Material Indices**Function Index**Tension (tie) Bending (beam) Bending (panel) Material Indices for Minimum Cost? Same for embodied energy Q = q, etc. mass = xV price [c ] = $/kg Total cost C = c x mass = c V Total cost C c [$/m3] [ c ] = [$/m3] “price density” Goal: minimisecost Performance metric = cost per given stiffness To minimise the cost Maximise Material Index ! IFB 2012 INTRODUCTION Material Indices**Comparative stiffness of panels of equal weight (Steel,**Ti, Al and Mg) (Emley, Principles of Mg Technology) IFB 2012 INTRODUCTION Material Indices**Function**Tie-rod Material Index Chose materials with largest M = Material for a stiff tie-rod of minimum mass { • Length L is specified • Must not deflect more than under load F Constraints • m = mass • = density E = Young’s modulus = deflection Equation for constraint on : ≤L = L /E = L F/AE A = Free variable ; or Trade-off variable Goal Minimise mass m: m = A L A = LF/E { What can be varied to meet the goal ? • Material • Cross section area A Performance metric: mass IFB 2012 INTRODUCTION Material Indices To minimise the mass Maximise Material Index !**Chose materials with largest M =**Materials for a strong, light beam Beam (shaped section). Function Area A Objective Minimise mass, m, where: Constraint Bending strength of the beam Mf: m = mass A = area L = length = density Mf = bending strength I = second moment of area E = Youngs Modulus Z = section modulus Combining the equations to eliminate A gives: IFB 2012 INTRODUCTION Material Indices To minimise the mass Maximise Material Index !**Failure of Beams; p. 535**IFB 2012 INTRODUCTION Material Indices**Moments of Sections; p 531**IFB 2012 INTRODUCTION Material Indices**Strong tie of length L and minimum mass**Tie-rod Function F F Area A L Objective (Goal) Minimise mass m: m = A L (2) m = mass A = area L = length = density = yield strength • Length L is specified • Must not fail under load F Constraints Eliminate A in (2) using (1): Free variables • Material choice • Section area A. Performance metric m Chose materials with largest M = Materials for a strong, light tie-rod Equation for constraint on A: F/A < y (1) IFB 2012 INTRODUCTION Material Indices To minimise the mass Maximise Material Index !**Sometimes a single property**• Sometimes a combination Either is a material index Function Stiffness Strength Tension (tie) Bending (beam) Bending (panel) Material Indices • An objective defines a performance metric: e.g. mass or cost. • The equation for the performance metric contains material properties. Example Objective: minimise mass Performance metric = mass IFB 2012 INTRODUCTION Material Indices**Function**Constraint Objective Free variable has a characterising material index Each combination of INDEX INDEX Maximise this! Material Indices Maximise this! IFB 2012 INTRODUCTION Material Indices**The End Introduction**IFB 2012 INTRODUCTION Material Indices