ISSUES TO ADDRESS - Eastern Mediterranean Universityme.emu.edu.tr/behzad/meng286/Mechanical...
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1
Chapter 8: Mechanical Failure ISSUES TO ADDRESS...
• How do cracks that lead to failure form?
• How is fracture resistance quantified? How do the fracture
resistances of the different material classes compare?
• How do we estimate the stress to fracture?
• How do loading rate, loading history, and temperature
affect the failure behavior of materials?
Ship-cyclic loading
from waves.
Computer chip-cyclic
thermal loading.
Hip implant-cyclic
loading from walking. Adapted from Fig. 22.30(b), Callister 7e.
(Fig. 22.30(b) is courtesy of National
Semiconductor Corporation.)
Adapted from Fig. 22.26(b),
Callister 7e. Adapted from chapter-opening photograph,
Chapter 8, Callister & Rethwisch 8e. (by
Neil Boenzi, The New York Times.)
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Fracture mechanisms • Ductile fracture
– Accompanied by significant plastic deformation
2
• Brittle fracture
– Little or no plastic deformation
– Catastrophic
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Ductile vs Brittle Failure
3
Very
Ductile
Moderately
Ductile Brittle
Fracture
behavior:
Large Moderate %AR or %EL Small
• Ductile fracture is
usually more desirable
than brittle fracture!
Adapted from Fig. 8.1,
Callister & Rethwisch 8e.
• Classification:
Ductile:
Warning before
fracture
Brittle:
No
warning
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DUCTILE FRACTURE
• Highly ductile materials – Pure gold and lead at room temperature, and other metals,
polymers, and inorganic glasses at elevated temperatures.
– They neck down to a point fracture
– Showing virtually 100% reduction in area.
4
• Moderate ductile fracture • The most common type of tensile fracture profile for ductile
materials
• Brittle fracture • Happens without any appreciable deformation and by rapid
crack growth
• The direction of crack growth is very nearly perpendicular to the
direction of the applied stress and yields a briefly flat surface.
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5
Example: Pipe Failures
• Ductile failure: -- one piece
-- large deformation
Figures from V.J. Colangelo and F.A.
Heiser, Analysis of Metallurgical Failures
(2nd ed.), Fig. 4.1(a) and (b), p. 66 John
Wiley and Sons, Inc., 1987. Used with
permission.
• Brittle failure: -- many pieces
-- small deformations
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6
Moderately Ductile Failure
• Resulting
fracture
surfaces
(steel)
50 mm
particles
serve as void
nucleation
sites.
50 mm
From V.J. Colangelo and F.A. Heiser,
Analysis of Metallurgical Failures (2nd
ed.), Fig. 11.28, p. 294, John Wiley and
Sons, Inc., 1987. (Orig. source: P.
Thornton, J. Mater. Sci., Vol. 6, 1971, pp.
347-56.)
100 mm
Fracture surface of tire cord wire
loaded in tension. Courtesy of F.
Roehrig, CC Technologies, Dublin,
OH. Used with permission.
• Failure Stages: necking
s
void nucleation
void growth and coalescence
shearing at surface
fracture
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Moderately Ductile vs. Brittle Failure
7
Adapted from Fig. 8.3, Callister & Rethwisch 8e.
cup-and-cone fracture brittle fracture
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Moderately Ductile Failure
8
– Occurs in several stages: 1) initial necking, 2) small cavity
formation, 3) coalescence of cavities to form a crack, 4)
crack propagation, 5) final shear fracture at a 45 angle
relative to the tensile direction
– 45° with the tensile axis is the angle at which the shear
stress is maximum
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Fractography-Ductile materials
9
– In a cop-and-cone fracture, the central interior region of the
surface has an irregular and fibrous appearance, which is
indicative of plastic deformation
– High magnification: consists of numerous spherical
“dimples”. Each dimple is one half of a microvoid that formed
and then separated during fracture process (elongated and
C-shaped).
Figure 8.4
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Fractography-Brittle materials
10
– In brittle fracture, the sign of gross plastic
deformation is absent. A series of V-shaped
“chevron” marking may form near the center of the
fracture cross section that point back toward the
crack initiation site.
– Other brittle fracture surfaces contain lines or ridges that
radiate from the origin of the crack in a fanlike pattern
– Brittle fracture in amorphous materials, such as
ceramic glasses, yields a relatively shiny and
smooth surface
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Brittle Failure
Arrows indicate point at which failure originated
11 Adapted from Fig. 8.5(a), Callister & Rethwisch 8e.
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CLEAVAGE FRACTURE
12
– For most brittle crystalline materials, crack
propagation corresponds to the successive and
repeated breaking of atomic bonds along specific
crystallographic planes (Cleavage).
– This type of fracture is transgranular (or
transcrystalline), as the fracture cracks pass
through the grains.
– Macroscopically, the fracture surface may have a
grainy or faceted texture, because the orientation
of the cleavage planes were changed from grain
to grain.
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13
Brittle Fracture Surfaces • Intergranular (between grains) 304 S. Steel
(metal) Reprinted w/permission
from "Metals Handbook",
9th ed, Fig. 633, p. 650.
Copyright 1985, ASM
International, Materials
Park, OH. (Micrograph by
J.R. Keiser and A.R.
Olsen, Oak Ridge
National Lab.)
Polypropylene
(polymer) Reprinted w/ permission
from R.W. Hertzberg,
"Defor-mation and
Fracture Mechanics of
Engineering Materials",
(4th ed.) Fig. 7.35(d), p.
303, John Wiley and
Sons, Inc., 1996.
4 mm
• Transgranular (through grains)
Al Oxide
(ceramic) Reprinted w/ permission
from "Failure Analysis of
Brittle Materials", p. 78.
Copyright 1990, The
American Ceramic
Society, Westerville, OH.
(Micrograph by R.M.
Gruver and H. Kirchner.)
316 S. Steel
(metal) Reprinted w/ permission
from "Metals Handbook",
9th ed, Fig. 650, p. 357.
Copyright 1985, ASM
International, Materials
Park, OH. (Micrograph by
D.R. Diercks, Argonne
National Lab.)
3 mm
160 mm
1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol.
3, ICF4, Waterloo, CA, 1977, p. 1119.)
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INETRGRANULAR FRACTURE
14
– Normally results subsequent to the occurrence of
processes that weaken or embrittle grain
boundary regions.
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15
Ideal vs Real Materials • Stress-strain behavior (Room T):
TS << TS engineering
materials
perfect
materials
s
e
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic typical strengthened metal typical polymer
• DaVinci (500 yrs ago!) observed... -- the longer the wire, the
smaller the load for failure.
• Reasons:
-- flaws cause premature failure.
-- larger samples contain longer flaws!
Reprinted w/
permission from R.W.
Hertzberg,
"Deformation and
Fracture Mechanics
of Engineering
Materials", (4th ed.)
Fig. 7.4. John Wiley
and Sons, Inc., 1996.
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STRESS CONCENTRATION
16
– Theoretical calculations of fracture strength is
based on atomic bonding energies.
– The measured fracture strengths of materials are
significantly lower than the theoretical values,
because of the presence of microvoid flaws or
cracks that always exist under normal conditions.
– The applied stress is amplified or concentrated at
the crack tips.
– The flaws are called stress risers
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Flaws are Stress Concentrators!
• Griffith Crack
where t = radius of curvature
so = applied stress
sm = stress at crack tip
17
t
Adapted from Fig. 8.8(a), Callister & Rethwisch 8e.
ott
om Ks
ss2/1
2a
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Concentration of Stress at Crack Tip
18
Adapted from Fig. 8.8(b),
Callister & Rethwisch 8e.
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ENGINEERING FRACTURE DESIGN
19
– Stress amplification is not restricted to these
microscopic defects, and may occur at
macroscopic internal discontinuities (e.g., voids or
inclusions), at sharp corers, scratches, and
notches.
– When the magnitude of a tensile stress at the tip
of one of the flaws exceeds the value of critical
stress, a crack forms and then propagate, which
result in fracture.
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ENGINEERING FRACTURE DESIGN
20
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Engineering Fracture Design
21
r/h
sharper fillet radius
increasing w/h
0 0.5 1.0 1.0
1.5
2.0
2.5
Stress Conc. Factor, K t =
• Avoid sharp corners! s
Adapted from Fig.
8.2W(c), Callister 6e.
(Fig. 8.2W(c) is from G.H.
Neugebauer, Prod. Eng.
(NY), Vol. 14, pp. 82-87
1943.)
r , fillet
radius
w
h
s max
smax
s0
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Crack Propagation
22
Cracks having sharp tips propagate easier than cracks
having blunt tips • A plastic material deforms at a crack tip, which
“blunts” the crack.
deformed region
brittle
Energy balance on the crack
• Elastic strain energy- • energy stored in material as it is elastically deformed
• this energy is released when the crack propagates
• creation of new surfaces requires energy
ductile
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Criterion for Crack Propagation
23
Crack propagates if crack-tip stress (sm) exceeds a critical stress (sc)
where – E = modulus of elasticity
– s = specific surface energy
– a = one half length of internal crack
For ductile materials => replace s with s + p
where p is plastic deformation energy
2/12
sas
cE
i.e., sm > sc
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Example – Brittle Fracture • Given Glass Sheet with
– Tensile Stress,
s = 40 Mpa
– E = 69 GPa
– = 0.3 J/m
• Find Maximum Length
of a
Surface Flaw
• Plan
• Set sc = 40Mpa
• Solve Griffith Eqn for
Edge-Crack Length
2
2
applied
sEa
s
Solving
µm2.8m102.8
N/m1040
N/m3.0N/m10692
6
226
29
a
a
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Fracture Toughness Ranges
25
Based on data in Table B.5,
Callister & Rethwisch 8e. Composite reinforcement geometry is: f
= fibers; sf = short fibers; w = whiskers;
p = particles. Addition data as noted
(vol. fraction of reinforcement): 1. (55vol%) ASM Handbook, Vol. 21, ASM Int.,
Materials Park, OH (2001) p. 606.
2. (55 vol%) Courtesy J. Cornie, MMC, Inc.,
Waltham, MA.
3. (30 vol%) P.F. Becher et al., Fracture
Mechanics of Ceramics, Vol. 7, Plenum Press
(1986). pp. 61-73.
4. Courtesy CoorsTek, Golden, CO.
5. (30 vol%) S.T. Buljan et al., "Development of
Ceramic Matrix Composites for Application in
Technology for Advanced Engines Program",
ORNL/Sub/85-22011/2, ORNL, 1992.
6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci.
Proc., Vol. 7 (1986) pp. 978-82.
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
5
K Ic
(MP
a ·
m 0.
5 )
1
Mg alloys
Al alloys
Ti alloys
Steels
Si crystal
Glass - soda
Concrete
Si carbide
PC
Glass 6
0.5
0.7
2
4
3
10
2 0
3 0
<100>
<111>
Diamond
PVC
PP
Polyester
PS
PET
C-C (|| fibers) 1
0.6
6 7
4 0
5 0 6 0 7 0
100
Al oxide Si nitride
C/C ( fibers) 1
Al/Al oxide(sf) 2
Al oxid/SiC(w) 3
Al oxid/ZrO 2 (p) 4
Si nitr/SiC(w) 5
Glass/SiC(w) 6
Y 2 O 3 /ZrO 2 (p) 4
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26
Design Against Crack Growth • Crack growth condition:
• Largest, most highly stressed cracks grow first!
K ≥ Kc = asY
--Scenario 1: Max. flaw
size dictates design stress.
maxas
YKc
design
s
amax no fracture
fracture
--Scenario 2: Design stress
dictates max. flaw size. 2
max1
s
design
c
YKa
amax
s no fracture
fracture
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27
Design Example: Aircraft Wing
Answer: MPa 168)( Bsc
• Two designs to consider...
Design A --largest flaw is 9 mm
--failure stress = 112 MPa
Design B --use same material
--largest flaw is 4 mm
--failure stress = ?
• Key point: Y and KIc are the same for both designs.
• Material has KIc = 26 MPa-m0.5
• Use... maxa
sY
KIcc
B max Amax aa cc ss
9 mm 112 MPa 4 mm --Result:
= a = sY
KIc constant
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Design using fracture mechanics
Example:
Compare the critical flaw sizes in the following metals subjected to
tensile stress 1500MPa and K = 1.12 sa.
KIc (MPa.m1/2)
Al 250
Steel 50
Zirconia(ZrO2) 2
Toughened Zirconia 12
Critical flaw size (microns)
7000
280
0.45
16
Where Y = 1.12. Substitute values
SOLUTION
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Impact Testing
31
final height initial height
• Impact loading: -- severe testing case
-- makes material more brittle
-- decreases toughness
Adapted from Fig. 8.12(b),
Callister & Rethwisch 8e. (Fig.
8.12(b) is adapted from H.W.
Hayden, W.G. Moffatt, and J.
Wulff, The Structure and
Properties of Materials, Vol. III,
Mechanical Behavior, John Wiley
and Sons, Inc. (1965) p. 13.)
(Charpy)
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32
Influence of Temperature on Impact Energy
Adapted from Fig. 8.15,
Callister & Rethwisch 8e.
• Ductile-to-Brittle Transition Temperature (DBTT)...
BCC metals (e.g., iron at T < 914ºC)
Imp
act E
ne
rgy
Temperature
High strength materials ( s y > E/150)
polymers
More Ductile Brittle
Ductile-to-brittle transition temperature
FCC metals (e.g., Cu, Ni)
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33
Design Strategy: Stay Above The DBTT!
• Pre-WWII: The Titanic • WWII: Liberty ships
• Problem: Steels were used having DBTT’s just below
room temperature.
Reprinted w/ permission from R.W. Hertzberg,
"Deformation and Fracture Mechanics of Engineering
Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and
Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard,
The Discovery of the Titanic.)
Reprinted w/ permission from R.W. Hertzberg,
"Deformation and Fracture Mechanics of Engineering
Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and
Sons, Inc., 1996. (Orig. source: Earl R. Parker,
"Behavior of Engineering Structures", Nat. Acad. Sci.,
Nat. Res. Council, John Wiley and Sons, Inc., NY,
1957.)
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FATIGUE
34
Adapted from Fig. 8.18,
Callister & Rethwisch 8e.
(Fig. 8.18 is from Materials
Science in Engineering, 4/E
by Carl. A. Keyser, Pearson
Education, Inc., Upper
Saddle River, NJ.)
• Fatigue = failure under applied cyclic stress.
• Stress varies with time. -- key parameters are S, sm, and
cycling frequency
S = stress amplitude
s max
s min
s
time
s m S
• Key points: Fatigue... --can cause part failure, even though smax < sy.
--responsible for ~ 90% of mechanical engineering failures.
-- occurs suddenly and catastrophically (brittle-like)
tension on bottom
compression on top
counter motor
flex coupling
specimen
bearing bearing
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Fatigue
35
Adapted from Fig. 8.17,
Callister & Rethwisch 8e.
• Fatigue = failure under applied cyclic stress.
• max and min stresses are
asymmetrical relative to the
zero stress
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Fatigue
36
Source: https://youtu.be/LhUclxBUV_E
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RANGE OF STRESS,STRESS
AMPLITUDE, AND STRESS RATIO
37
• Mean stress
• Range of stresses
• One-half of the range
(stress amplitude)
• Stress ratio
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Question
38
• make a schematic sketch of a stress-versus-time plot
for the situation when the stress ratio R has a value of
+1.
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39
Types of Fatigue Behavior
Adapted from Fig.
8.19(a), Callister &
Rethwisch 8e.
• Fatigue limit, Sfat: --no fatigue if S < Sfat
Sfat
case for steel (typ.)
N = Cycles to failure 10
3 10
5 10
7 10
9
unsafe
safe
S =
str
ess a
mplit
ude
• For some materials,
there is no fatigue
limit!
Adapted from Fig.
8.19(b), Callister &
Rethwisch 8e.
case for Al (typ.)
N = Cycles to failure 10
3 10
5 10
7 10
9
unsafe
safe
S =
str
ess a
mplit
ude
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CREEP
40
• time-dependent and permanent deformation of
materials when subjected to constant load or stress
• normally an undesirable phenomenon and reduces the
lifetime of the mechanical parts
• for metals, it becomes important at T>0.4Tm (absolute
temperature)
• amorphous polymers are specially sensitive to creep
deformation
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CREEP Sample deformation at a constant load or stress (s) vs. time
(T = constant)
41
Adapted from
Fig. 8.28, Callister &
Rethwisch 8e.
Primary Creep: slope (creep rate)
decreases with time.
Secondary Creep: steady-state
i.e., constant slope De/Dt).
Tertiary Creep: slope (creep rate)
increases with time, i.e. acceleration of rate.
s
s,e
0 t
elastic deformation
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CREEP CURVE
42
• Primary region: the material is experiencing an
increase in creep resistance or strain hardening (the
deformation becomes more difficult as the material is
strained)
• Secondary region: the longest duration ( a balance
between the competing processes of strain hardening
and recovery)
• Tertiary region: the acceleration of the rate of creep.
The failure is termed “rupture”
•
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ENGINEERING DESINS
43
• in the long-life applications (e.g., nuclear power plant),
De/Dt) is the most important parameter from a creep
rupture test.
• in short-life creep situations (e.g., turbine blades), time
to rupture or rupture lifetime is the dominant design
consideration.
•
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UNDERESTANDING CREEP
44
Source: https://youtu.be/opPWceW-YKc
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45
Creep: Temperature Dependence
• Occurs at elevated temperature, T > 0.4 Tm (in K)
Adapted from Fig. 8.29,
Callister & Rethwisch 8e.
elastic
primary secondary
tertiary
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Creep: Temperature Dependence
46
• with either increasing stress or temperature:
• the instantaneous strain at the tie of stress application
increases
• the steady-state creep rate is increased
• the rupture life is diminished
•
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47
Secondary Creep • Strain rate is constant at a given T, s
-- strain hardening is balanced by recovery
stress exponent (material parameter)
strain rate
activation energy for creep
(material parameter)
applied stress material const.
• Strain rate
increases
with increasing
T, s
10
2 0
4 0
10 0
2 0 0
10 -2 10 -1 1
Steady state creep rate (%/1000hr) e s
Str
ess (
MP
a) 427ºC
538ºC
649ºC
Adapted from
Fig. 8.31, Callister 7e.
(Fig. 8.31 is from Metals
Handbook: Properties
and Selection:
Stainless Steels, Tool
Materials, and Special
Purpose Metals, Vol. 3,
9th ed., D. Benjamin
(Senior Ed.), American
Society for Metals,
1980, p. 131.)
se
RTQ
K cns exp2
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Prediction of Creep Rupture Lifetime
48
• prolonged creep tests are sometimes not practical!
• one solution is to perform creep rupture tests at
temperatures in excess of those required, for shorter
time periods, and at a comparable stress level, and
then making a suitable extrapolation to the in-service
condition.
• a common extrapolation procedure is Larson-Miller
parameter.
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Prediction of Creep Rupture Lifetime • Estimate rupture time S-590 Iron, T = 800ºC, s = 20,000 psi
time to failure (rupture)
function of
applied stress
temperature
LtT r )log20(
Time to rupture, tr
310x24)log20)(K 1073( rt
Ans: tr = 233 hr Adapted from Fig. 8.32, Callister & Rethwisch
8e. (Fig. 8.32 is from F.R. Larson and J.
Miller, Trans. ASME, 74, 765 (1952).)
103 L (K-h)
Str
ess (
10
3 p
si)
100
10
1 12 20 24 28 16
data for
S-590 Iron
20
24
49
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Estimate the rupture time for S-590 Iron, T = 750ºC, s = 20,000 psi
• Solution:
50 50
Adapted from Fig. 8.32, Callister & Rethwisch
8e. (Fig. 8.32 is from F.R. Larson and J.
Miller, Trans. ASME, 74, 765 (1952).)
103 L (K-h)
Str
ess (
10
3 p
si)
100
10
1 12 20 24 28 16
data for
S-590 Iron
20
24
310x24)log20)(K 1023( rt
Ans: tr = 2890 hr
time to failure (rupture)
function of
applied stress
temperature
LtT r )log20(
Time to rupture, tr
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51
SUMMARY • Failure type depends on T and s :
-For simple fracture (noncyclic s and T < 0.4Tm), failure stress
decreases with:
- increased maximum flaw size,
- decreased T,
- increased rate of loading.
- For fatigue (cyclic s:
- cycles to fail decreases as Ds increases.
- For creep (T > 0.4Tm):
- time to rupture decreases as s or T increases.