Caceres-L3 Understanding Materials Selection Charts

MECH4301 2008 Lecture 3

Charts 1/19

Lecture 3Understanding Material Selection Charts (2/2)

MECH4301 2008 Materials Selection in Mechanical Design

•Fracture Toughness - Elastic Modulus Chart (p. 59)

•Fracture Toughness - Strength Chart (p. 61)


Charts 2/19

Fracture toughness vs Young’s modulus: stiffness is important provided the material does not crack or snap under load. Toug

h and stiff

Rubber =>

polymers=>metals

=>ceramics

Deflects a lot without breaking (hinges, snap-on lids)

Stiff but brittle

E (GPa

)

KIc

(MPa m1/2)

aK *IC


Charts 3/19

Fracture toughness vs Young’s modulus:

cEGK IC

aK *IC

Metals: KIC > 15 MPa

m1/2

(Minimum for safe design, p.136)

Contours of

equal Gc=K2

Ic/E (slope

0.5)

Lower limit for

KIC

Contours of equal KIc/E (slope 1)

E

KG Ic

c

2


Charts 4/19

Contour/Selection Lines in KIc- E chart4 lines of interest in the KIc- E chart: Lower limit for KIc ?

Contour lines of constant KIc ?

Contour lines at constant KIc2/E ?

Contour lines at constant KIc/E ?

Next slide

3 Case studies


Charts 5/19

ro = 2 x 10-10 m (interatomic spacing)

Lower limit for perfectly brittle materials Ceramics & glasses nearly touch the

boundary

Lower limit to KIc

Emxr

EK oIc

2/162/1

10310

cEGK IC

2/1o

2/1o

c 10

r

20

2r 22 G

EEEK Ic

20oEr

aK *IC


Charts 6/19

Contour lines: Case studies involving KIc-EThree case studies (textbook, p. 136;

Question 3.11, Tute 1, p. 561):

1. Load limited design (component should take

specified load w/o failure, e.g.: tension members in

cantilever bridge)

2. Displacement limited design (Component

must deflect a given amount w/o failure, e.g.: bottle

snap-on lids)

3. Energy absorption controlled design (component must absorb specified amount of energy

prior to failure, e.g.: car bumper)


Charts 7/19

Case study 1: Load limited design (component should take specified load without failure, trivial case) (p. 137)

a

K Ic

*

To increase * for given

a, increase

KIc

aK *IC

Application: anything supporting a tensile load


Charts 8/19

Case study 2: Displacement limited design (Component must deflect a given amount without failure) (p.138)

a

K Ic

*

E

Kconst

a

K

EEIcIc .

1**


a, increase

KIc/E

F Fa

Elastic strain at failure?

* = E * (Hooke’s law)

E

K Ic*


Charts 9/19

Case study 2 (cont’d.) : Displacement limited design (p. 138) Component must deflect a given amount without failure)


a, increase

KIc/E

E

K Ic* Application: hinges, plastic snap-on lids

Question 3.11, Tute 1


Charts 10/19

Process

zone

Case study 3: Energy absorption controlled design (p. 137) (component must absorb specified amount of energy prior to failure)

E

KG Ic

c

2

To increase energy

absorption prior to

fracture, pick materials with high values of

(KIc)2 /E

F FacEGK IC

Application: car bumper

Also called J- integral


Charts 11/19

Conclusion: Fracture toughness vs. Young’s modulus

Load limited design

(K)K K/E K2/E

Metals

Polym

Ceram

Displacement limited design

(K/E)

Energy limited design (K2/E)

Polymers beat ceramics despite their low K because of their

high Gc and low E (K/E=Gc/E1/2; K2/E=Gc)


Charts 12/19

Fracture toughness vs strength: strength is important provided the material does not crack under load.

Tough and strong

Foams=>Rubber =

>

Polymers=

>Metals

=>Ceramics

Yield before fracture (ductile materials)

Fracture before yield (brittle materials)

YS (MPa)

KIc

(MPa m1/2)

Yield before fracture

Leak before fracture


Charts 13/19

Fracture toughness vs strength: strength is important provided the material does not crack under load.

Contours of equal process zone or “crack

size”

aK *IC

21

y

IcKa


Charts 14/19

Case studies in KIc- : Pressure vesselsTwo case studies (p. 140 in textbook,

Question 3.12, Tute 1, p 561):

1. Yield before break, or why you can forget you

coke/beer can in the freezer and nothing happens. Small

vessels.

2. Leak before break, or why nuclear reactors

don’t go bust (most of of the time, anyway.) Large

vessels.


Charts 15/19

Small pressure vessels: Yield before break

yt

PR 2

a

K Ic

*

P a < t

crack aK *IC

Y.B.B. => y < *

21

y

IcKa

To maximise size of safe crack, pick

materials with high K/y ratio

t


Charts 16/19

Crack size increases this

way

Small pressure vessels: Yield before break

21

y

IcKa


Charts 17/19

Large pressure vessels: Leak before break

R

tP y2

2

*

t

K

a

K IcIc

y

PRt

2Set 2a = t

(vessel leaks)

2 **IC taK

2

22*

t

KIc

PR

K yIc

2

2* 4

y

Ic

R

KP

24

y *set

To maximise operating pressure, pick materials

with high K2/y ratio

Crack still stable at yield

Maximum pressure

Eliminate t

To minimise wall thickness,

maximise y


Charts 18/19

Operating pressure

increases this way

Large pressure vessels: Leak before break

y

IcKP

2

y

PRt

2

Wall thickness decreases this

way

Pressure vessel steels


Charts 19/19

End of Lecture 3


Charts 20/19

Question 3.21 : production energy is embodied energy * density => q* (MJ/m3)

MaterialUniverse:\ Metals and alloys MaterialUniverse:\ Hybrids: composites, foams, natural materials

MaterialUniverse:\ Polymers and elastomers

MaterialUniverse:\ Metals and alloysMaterialUniverse:\ Hybrids: composites, foams, natural materialsMaterialUniverse:\ Polymers and elastomers

Densi

ty *

Em

bodie

d e

nerg

y, p

rim

ary

pro

duct

ion

1000

10000

100000

1e6

1e7

1e8

1e9

Cast aluminum alloy,ABS (High-impact, Injection Molding)

GFRPWhy do we plot

*q instead of

just q ?


Charts 21/19

Modulus - Density chartE

E

CR

Modulus- Relative Cost chart (relative to iron)

Why do we

plot CR

instead of

just CR?


Charts 22/19

Modulus - Production energy chart (Embodied energy)

Why do we plot

Hq instead of

just Hq ?

E

Hq


Charts 23/19

Mass m (kg) proportional to density, (kg/m-3) COST: Cost per unit mass c ($/kg) Total cost, C ($), for mass m The Total Cost C is proportional to c ($/m3)

( c = “cost” density)

Hq = production energy per unit mass (MJ/kg)

The total production energy Q

The total Q is proportional to Hq (MJ/ m3)

( Hq = density of “production energy”)

ccVcmC

Vm

q HHVHmQ

qq

Tute 1, Exercises 19 and 21)

Why do we plot CR and Hq instead of just

CR or Hq ?

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Caceres-L3 Understanding Materials Selection Charts