caceres-l3 understanding materials selection charts
TRANSCRIPT
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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)
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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)
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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**
To increase * for given
a, increase
KIc/E
F Fa
Elastic strain at failure?
* = E * (Hooke’s law)
E
K Ic*
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MECH4301 2008 Lecture 3
Charts 9/19
Case study 2 (cont’d.) : Displacement limited design (p. 138) Component must deflect a given amount without failure)
To increase * for given
a, increase
KIc/E
E
K Ic* Application: hinges, plastic snap-on lids
Question 3.11, Tute 1
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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)
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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.
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
Charts 16/19
Crack size increases this
way
Small pressure vessels: Yield before break
21
y
IcKa
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
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
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MECH4301 2008 Lecture 3
Charts 19/19
End of Lecture 3
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MECH4301 2008 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 ?
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MECH4301 2008 Lecture 3
Charts 21/19
Modulus - Density chartE
E
CR
Modulus- Relative Cost chart (relative to iron)
Why do we
plot CR
instead of
just CR?
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MECH4301 2008 Lecture 3
Charts 22/19
Modulus - Production energy chart (Embodied energy)
Why do we plot
Hq instead of
just Hq ?
E
Hq
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MECH4301 2008 Lecture 3
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
Tute 1, Exercises 19 and 21)
Why do we plot CR and Hq instead of just
CR or Hq ?