advanced methods in materials selection
Download
Skip this Video
Download Presentation
Advanced Methods in Materials Selection

Loading in 2 Seconds...

play fullscreen
1 / 29

Advanced Methods in Materials Selection - PowerPoint PPT Presentation


  • 56 Views
  • Uploaded on

Advanced Methods in Materials Selection. Conflicting Constraints Lecture 2 & Tutorial 2. IFB Lecture 2: Textbook Chapters 7 & 8. Conflicting Constraints. Fork for a pushbike: what is more important, strength or stiffness?. Stiffness dominated design versus Strength dominated design.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Advanced Methods in Materials Selection' - lacey-roberson


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
advanced methods in materials selection

Advanced Methods in Materials Selection

  • Conflicting Constraints
  • Lecture 2 & Tutorial 2

IFB 2012 Conflicting Constraints

slide2

IFB Lecture 2: Textbook Chapters 7 & 8

IFB 2012 Conflicting Constraints

conflicting constraints
Conflicting Constraints

Fork for a pushbike:

what is more important, strength or stiffness?

  • Stiffness dominated design
  • versus
  • Strength dominated design

IFB 2012 Conflicting Constraints

outline lecture 2
Outline Lecture 2
  • Conflicting constraints:
  • “most restrictive constraint wins”
  • Case study 1: Stiff / strong / light tie rod
  • Case study 2: Safe (no yield - no fracture)/ light air tank for a truck

IFB 2012 Conflicting Constraints

slide5

Most designs are over-constrained: “Should not deflect more than something, must not fail by yielding, by fatigue, by fast-fracture …” more constraints than free variables

IFB 2012 Conflicting Constraints

e8 1 materials for a stiff light tie rod constraint 1

Strong tie of length L and minimum mass

Function

Tie-rod

F

F

Area A

L

Minimise mass m:

m = A L  (2)

Objective

  • Length L is specified
  • Must not stretch more than 

Constraints

Free variables

  • Material choice
  • Section area A

Performance metric m1

E8.1. Materials for a stiff, light tie-rod Constraint # 1

m = mass

A = area

L = length

 = density

E= elastic modulus

 = elastic deflection

Equation for constraint on A:

 = L = L/E = LF/AE (1)

Eliminate A in (2) using (1):

Chose materials with largest M1 =

IFB 2012 Conflicting Constraints

e8 1 materials for a strong light tie rod constraint 2

Strong tie of length L and minimum mass

Function

Tie-rod

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

Chose materials with largest M2 =

Performance metric m2

E8.1. Materials for a strong, light tie-rod Constraint # 2

Equation for constraint on A:

F/A < y (1)

IFB 2012 Conflicting Constraints

e8 1 conflicting constraints strong stiff light tie rod

= deflection

y = yield strength

  • E = elastic modulus

Max. deflection

Must not yield

Competing

performance metrics

E8.1: Conflicting Constraints: Strong /Stiff / Light Tie Rod

Requires stiffer material

Evaluate competing constraints and performance metrics:

Stiffness constraint

Strength constraint

Rank by the more restrictive of the two, meaning…?

IFB 2012 Conflicting Constraints

analytical solution in three steps rank by the more restrictive of the constraints
Analytical solution in three steps: Rank by the more restrictive of the constraints

1. Calculate m1 and m2 for given L (1 m) and F (10 kN)

2. Find the largest of every pair of m’s

3. Find the smallest of the larger ones

The most restrictive constraint requires a larger mass  activeconstraint.

Cons to the analytical solution: Solution is not general, as it is a function of L, δ and F. (I.e., the above solution represents only the particular values of L, δ and F used in the calculations.)Lacks visual immediacy.

IFB 2012 Conflicting Constraints

graphical version of the analytical solution for aluminium

mass

/L= 0.1%:y constraint active (heavier) for short rods

length

Graphical version of the analytical solution (for Aluminium)

/L= 0.1%:E constraint active (heavier) for long rods (rod stretches too much)

IFB 2012 Conflicting Constraints

slide11

Pros to the graphical-analytical solution (Slide #10): it makes explicit the dependence on L and L/.Cons: it is specific to the material considered (requires a dedicated graph per material)

Cons to the analytical solution (slide #9) (more restrictive constraint) Solution is not general, as it is function of L, δ and F Lacks visual immediacy.

Graphical solution using indices and bubble charts:

  • More general/powerful. Changes in L, δ and F are easily visualised
  • Allows for a visual while physically based selection.
  • Involves all available materials.
  • Incorporates geometrical constraints through coupling factors.

IFB 2012 Conflicting Constraints

graphical solution using indices and bubble charts

M1 =

M2=

Graphicalsolution using Indices and Bubble charts

This is what we know

make m1= m2

Solve for M1

Straight line, slope = 1 y-intcpt = L/

IFB 2012 Conflicting Constraints

e 8 1 tie rod graphical solution l 1 l 100 use level 3 exclude ceramics

m1 = m2

E 8.1 Tie Rod Graphical solution (/L = 1% => L/ = 100) Use level 3, exclude ceramics

Simultaneously Maximise M1 and M2

m1 < m2

Coupling line for L/ = 100

m2 < m1

IFB 2012 Conflicting Constraints

e8 1 tie rod graphical solution l 0 1 l 1000 use level 3 exclude ceramics

Coupling line for L/ = 1000

E8.1 Tie Rod Graphical solution( /L = 0.1% => L/=1000) Use level 3, exclude ceramics

Active Constraint? 3-D view

Coupling line for L/ = 100

IFB 2012 Conflicting Constraints

3 d view of the interacting constraints

m1 = m2

lighter

3-D view of the interacting constraints

m1

m2

m1 > m2

m2 > m1

Locus of coupling line depends on coupling factor

  • m1 = m2 on the coupling line.
  • The closer to the bottom corner, the lighter the component.
  • Away from the coupling line, one of the constraints is active (larger m)

IFB 2012 Conflicting Constraints

graphical solution deflection 1 l 100

lighter

m1 = m2

Graphical solution (deflection = 1% L/=100)

m1 < m2

Coupling line for L/ = 100

m2 < m1

IFB 2012 Conflicting Constraints

case study 2 quite similar to e8 2 t ute 2 air cylinder for a truck

Compressed air tank

Case Study # 2: Quite Similar to E8.2 (Tute 2), Air cylinder for a truck

Design goal: lighter, safe air cylinders for trucks

IFB 2012 Conflicting Constraints

case study air cylinder for truck

t

Density 

Yield strength y

Fracture toughness K1c

Pressure p

2R

FunctionPressure vessel

Objective Minimise mass

ConstraintsDimensions L, R, pressure p, given

Safety: must not fail by yielding

Safety: must not fail by fast fracture

Must not corrode in water or oil

Working temperature -50 to +1000C

Wall thickness, t; choice of material

L

Conflicting constraints lead to competing performance metrics

Free variables

Case study: Air cylinder for truck

IFB 2012 Conflicting Constraints

air cylinder for truck

t

Density 

Yield strength y

Fracture toughness K1c

Pressure p

2R

L

Aspect ratio, 

Vol of material in cylinder wall

Objective: mass

Failure stress

Stress in cylinder wall

Safety factor

Eliminate t

transpose

Air cylinder for truck

What is the free variable?

May be either y or f!

IFB 2012 Conflicting Constraints

air cylinder graphical solution using ces charts

CES Stage 2: evaluate conflicting performance metrics:

S = safety factor

a = crack length

y = yield strength

K1c = Fracture toughness

Must not yield:

Must not fracture

Competing

performance metrics

for minimum mass

Air cylinder : graphical solution using CES charts

CES Stage 1; apply simple (non conflicting) constraints:

working temp up to 1000C, resist organic solvents etc.

Equate m1 to m2, and find the coupling factor for given crack size a.

IFB 2012 Conflicting Constraints

air cylinder simple non conflicting constraints

Max service temp

= 373 K (1000C)

Corrosion resistance in organic solvents

Corrosion resistance

Air cylinder - Simple (non- conflicting) constraints
  • CES Stage 1:
  • Impose constraints on corrosion in organic solvents
  • Impose constraint on maximum working temperature

Select above this line

IFB 2012 Conflicting Constraints

ces stage 2 equate m 1 to m 2 and find the coupling factor for given crack size a
CES, Stage 2: Equate m1 to m2, and find the coupling factor for given crack size a.

=

=

for a crack a = 5 mm, the coupling factor is 1/√(3.14*0.005) = 1/0.12 = 8

IFB 2012 Conflicting Constraints

air cylinder conflicting constraints

Results so far:

  • Epoxy/carbon fibre composites
  • Epoxy/glass fibre composites
  • Low alloy steels
  • Titanium alloys
  • Wrought aluminium alloy
  • Wrought austenitic stainless steels
  • Wrought precipitation hardened stainless steels

Lighter this way

CES Stage 2: Find most restrictive constraint using Material Indices chart

Air cylinder - Conflicting constraints

a = 5 mm intcpt= 8

@ 1/M1= 1

Repeat for a = 5 μm

IFB 2012 Conflicting Constraints

summary
Summary
  • Most designs are over-constrained and many have multiple objectives
  • Method of maximum restrictiveness copes with conflicting multiple constraints
  • Analytical method useful but depends on the particular conditions set and lacks the visual power of the graphical method
  • Graphical method produces a more general solution
  • Next lecture will solve case studies for two conflicting objectives: e.g., weight and cost.

IFB 2012 Conflicting Constraints

solutions to e8 2
Solutions to E8.2

Exercises for Tutorial on multiple constraints

  • 8.2 a Coupling factor = 253 for c= 5 µm;
  • 8.2 b Coupling factor = 8 for c = 5 mm.

1- Textbook Exercise 8.2, p. 616

2- Exercise on slide # 27

IFB 2012 Conflicting Constraints

there is a typographical error in your textbook exercise e8 2 p 616 6 lines from the top
There is a typographical error in your textbook, Exercise E8.2,p. 616, 6 lines from the top

It reads:

It should read:

IFB 2012 Conflicting Constraints

exercise 2 for tutorial on multiple constraints
Exercise 2 for Tutorial on multiple constraints

IFB 2012 Conflicting Constraints

exercise 2 for tutorial on multiple constraints1
Exercise 2 for Tutorial on multiple constraints
  • Hypothetical values to fix the coupling line

IFB 2012 Conflicting Constraints

slide29

End of IFB Lecture 2

IFB 2012 Conflicting Constraints

ad