Caceres-L3 Understanding Materials Selection Charts
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Transcript of 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)
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
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
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
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
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)
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
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*
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
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
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)
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
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
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.
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
MECH4301 2008 Lecture 3
Charts 16/19
Crack size increases this
way
Small pressure vessels: Yield before break
21
y
IcKa
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
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
MECH4301 2008 Lecture 3
Charts 19/19
End of Lecture 3
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 ?
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?
MECH4301 2008 Lecture 3
Charts 22/19
Modulus - Production energy chart (Embodied energy)
Why do we plot
Hq instead of
just Hq ?
E
Hq
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 ?