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Transcript of [email protected] ENGR-45_Lec-19_Failure-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of...
[email protected] • ENGR-45_Lec-19_Failure-1.ppt1
Bruce Mayer, PE Engineering-45: Materials of Engineering
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Engineering 45
MaterialMaterialFailure Failure
(1)(1)
[email protected] • ENGR-45_Lec-19_Failure-1.ppt2
Bruce Mayer, PE Engineering-45: Materials of Engineering
Learning Goals.1 – FailureLearning Goals.1 – Failure
How Flaws In A Material Initiate Failure How Fracture Resistance is Quantified
• How Different Material Classes Compare
How to Estimate The Stress at Fracture Factors that Change the Failure Stress
• Loading Rate
• Loading History
• Temperature
[email protected] • ENGR-45_Lec-19_Failure-1.ppt3
Bruce Mayer, PE Engineering-45: Materials of Engineering
Learning Goals.2 – FailureLearning Goals.2 – Failure
FATIGUE Failure• Fatigue Limit
• Fatigue Strength
• Fatigue Life
CREEP at Elevated Temperatures• Incremental Yielding at <σy Over a Long
Time Period at Elevated Temperature
[email protected] • ENGR-45_Lec-19_Failure-1.ppt4
Bruce Mayer, PE Engineering-45: Materials of Engineering
Ductile vs Brittle Fracture Ductile vs Brittle Fracture
• Classification:
• Ductile fracture is desirable!
Ductile: warning before
fracture
Brittle: No
warning
Very Ductile
Moderately Ductile BrittleFracture
behavior:
Large Moderate%Ra or %EL: Small• Ductility:
[email protected] • ENGR-45_Lec-19_Failure-1.ppt5
Bruce Mayer, PE Engineering-45: Materials of Engineering
Example: Pipe Failure Example: Pipe Failure Ductile Failure
• One Piece
• Large Deformation
• LEAK before BURST
Brittle Failure• Many Pieces
• Small Deformation
• EXPLOSIVE Burst– NOT Good
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.
[email protected] • ENGR-45_Lec-19_Failure-1.ppt6
Bruce Mayer, PE Engineering-45: Materials of Engineering
Fracture FormationFracture Formation Fracture Formation
Steps1. Crack Initiation
2. Crack Propagation
DUCTILE Fracture• Significant PLASTIC
Deform. at Crack Tip
• Crack(s) Grow Relatively Slowly
BRITTLE Fracture
• Once Brittle-Crack Starts Propagation can NOT be stopped– Can Proceed at
Speeds up toMACH-1
[email protected] • ENGR-45_Lec-19_Failure-1.ppt7
Bruce Mayer, PE Engineering-45: Materials of Engineering
Moderately Ductile Fracture Moderately Ductile Fracture Stages to Fracture upon Loadingnecking void
nucleationvoid growth and linkage
shearing at surface
fracture
Resulting fracture surfaces (steel)
50 m50 m
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.)
Particles serve as void nucleation sites
100 m
Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.
[email protected] • ENGR-45_Lec-19_Failure-1.ppt8
Bruce Mayer, PE Engineering-45: Materials of Engineering
Ductile vs. Brittle Tensile FailureDuctile vs. Brittle Tensile Failure Ductile Failure
“Cup-and-Cone” Fracture Surface
Brittle Failure
“Matted” Fracture Surface
[email protected] • ENGR-45_Lec-19_Failure-1.ppt9
Bruce Mayer, PE Engineering-45: Materials of Engineering
Brittle-Fracture SurfacesBrittle-Fracture Surfaces• Intergranular(between grains)
• Intragranular (within/across 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.)
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, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons, Inc., 1996.
3m
4 mm160m
1 mm
[email protected] • ENGR-45_Lec-19_Failure-1.ppt10
Bruce Mayer, PE Engineering-45: Materials of Engineering
Brittle-FractureBrittle-Fracture Characteristics of Brittle
Fracture • No Significant Deformation
• Proceeds by Rapid Crack Propagation
• Crack Direction Almost to Applied Load
• Relatively Flat Fracture Surface
[email protected] • ENGR-45_Lec-19_Failure-1.ppt11
Bruce Mayer, PE Engineering-45: Materials of Engineering
6
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.
Ideal vs Real materialsIdeal vs Real materials
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic typical strengthened metaltypical polymer
MaterialsPerfect
MaterialsgEngineerin TSTS
Rm-Temp Stress-Strain Behavior
• DaVinci (500 yrs ago!) Observed– The LONGER the Wire, the
SMALLER to Load Needed to Cause Failure
• Reasons– Matl Flaws Cause Premature Failure– Larger samples have more flaws
[email protected] • ENGR-45_Lec-19_Failure-1.ppt12
Bruce Mayer, PE Engineering-45: Materials of Engineering
Stress ConcentrationStress Concentration Elliptical hole in a plate: σ distrib. in front of hole:
o
2a
max
t
2o
a 1
t
Define Stress Concentration Factor:
Kt max /o
Large Kt Promotes Facture-Failure
NOT SO BAD
Kt=3 BAD! Kt>>3
ρt Local Hole,or CrackTip,
Radius
[email protected] • ENGR-45_Lec-19_Failure-1.ppt13
Bruce Mayer, PE Engineering-45: Materials of Engineering
8
• Avoid sharp corners!Engineering Fracture DesignEngineering Fracture Design
r= FilletRadius
w
h
o
max
r/h
sharper fillet radius
increasing w/h
0 0.5 1.01.0
1.5
2.0
2.5
Stress Conc. Factor, Ktmaxo
=
[email protected] • ENGR-45_Lec-19_Failure-1.ppt14
Bruce Mayer, PE Engineering-45: Materials of Engineering
Griffith Theory of Brittle FractureGriffith Theory of Brittle Fracture A. A. Griffith (1920s)
proposed that very small, MICROSCOPIC cracks weaken brittle materials• This is why the theoretical
Tensile strength of a brittle elastic solid (~E/10) is not achieved
Griffith proposed that all brittle materials contain a POPULATION of small cracks and flaws that have a VARIETY of sizes, shapes, and orientations
Fracture occurs when the THEORETICAL cohesive strength of the material is exceeded at the TIP of one of these flaws• This was shown with glass,
where very fine and super-strong WHISKERS were shown to have strengths CLOSE to the THEORETICAL
• However, larger samples very quickly form surface flaws, and the strength drops!
[email protected] • ENGR-45_Lec-19_Failure-1.ppt15
Bruce Mayer, PE Engineering-45: Materials of Engineering
Glass Rod Bending FractureGlass Rod Bending Fracture
Cantilever-Load on Glass Rod
Load to Failure by Brittle Fracture
The Fracture Surface The Facture Surface
displays 3, more or less, Distinct Regions
[email protected] • ENGR-45_Lec-19_Failure-1.ppt16
Bruce Mayer, PE Engineering-45: Materials of Engineering
Glass Rod Bending FractureGlass Rod Bending Fracture
Mirror Zone A smooth region surrounding the fracture origin Mist Zone A small band of rougher surface surrounding the
mirror region. Hackle Zone Area composed of large irregularly oriented facets.
[email protected] • ENGR-45_Lec-19_Failure-1.ppt17
Bruce Mayer, PE Engineering-45: Materials of Engineering
Crack PropagationCrack Propagation Cracks propagate due to SHARPNESS
of the crack tip A PLASTIC material DEFORMS at the tip,
“blunting” the crack
plasticBrittle
DeformedRegion
Perform Energy balance on the crack• Elastic 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
[email protected] • ENGR-45_Lec-19_Failure-1.ppt18
Bruce Mayer, PE Engineering-45: Materials of Engineering
Griffith Brittle-Fracture TheoryGriffith Brittle-Fracture Theory When a Crack
Propagates• There is a RELEASE
of Elastic Strain Energy
• There is Energy CONSUMED To Extend The Crack By Creating NEW Fracture Surfaces
Griffith’s Proposal for Crack Propagation
• Propagation Requires – [release of elastic strain
energy] > [energy required to form new crack surfaces]
aE s
c 2
c Critical Stress for Crack Propagation (Pa)
– E Elastic Modulus (Pa)
s Surface Energy (J/m)
– a Crack Length(m)
[email protected] • ENGR-45_Lec-19_Failure-1.ppt19
Bruce Mayer, PE Engineering-45: Materials of Engineering
Example – Brittle FractureExample – Brittle Fracture Given Glass Sheet
with• Tensile Stress,
= 40 Mpa
• E = 69 GPa = 0.3 J/m
Find Maximum Length of a Surface Flaw
Plan
• Set c = 40Mpa
• Solve Griffith Eqn for Edge-Crack Length
2
2
applied
sEa
Solving
µm2.8m102.8
N/m1040
N/m3.0N/m10692
6
226
29
a
a
[email protected] • ENGR-45_Lec-19_Failure-1.ppt20
Bruce Mayer, PE Engineering-45: Materials of Engineering
When Does a Crack Propagate? When Does a Crack Propagate? The Crack Tip
Radius, ρt, canbe Quite Small
Thus σCrk-Tip can be Very Large
distance, x, from crack tip
tip K2 a
tip
increasing K
Crack propagates when the tip stress is large enough to make:
K ≥ Kc• Kc Fracture Toughness
(MPa•m)– Cool units
[email protected] • ENGR-45_Lec-19_Failure-1.ppt21
Bruce Mayer, PE Engineering-45: Materials of Engineering
K, KK, Kcc: Geometry, Load, Matl : Geometry, Load, Matl Recall Condition for Crack Propagation
• Values of K for Some Standard Loads & Geometries
K ≥ KcStress Intensity Factor:--Depends on load & geometry.
Fracture Toughness:--Depends on the material, temperature, environment, & rate of loading.
2a2a
inksior
mMPa
:Kofunits
aa K a K 1.1 a
[email protected] • ENGR-45_Lec-19_Failure-1.ppt22
Bruce Mayer, PE Engineering-45: Materials of Engineering
Crack Extension Modes Crack Extension Modes Cracks can Extend in 3 Modes: I, II, III
Combination of Modes Can Occur; Particularly Modes I+III (think Drive Shaft)
Mode-I is By Far the Most Common
• Mode-I: Opening Mode
• Mode-II: Shearing or Sliding Mode
• Mode-III: Tearing or AntiPlane Mode
[email protected] • ENGR-45_Lec-19_Failure-1.ppt23
Bruce Mayer, PE Engineering-45: Materials of Engineering
KKIIcc for Several Metals for Several Metals Higher Values
of KIc are Desired
[email protected] • ENGR-45_Lec-19_Failure-1.ppt24
Bruce Mayer, PE Engineering-45: Materials of Engineering
11
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
5
KIc
(MPa
· m
0.5)
1
Mg alloysAl alloys
Ti alloys
Steels
Si crystalGlass -soda
Concrete
Si carbide
PC
Glass 6
0.5
0.7
2
4
3
10
20
30
<100>
<111>
Diamond
PVC
PP
Polyester
PS
PET
C-C(|| fibers)1
0.6
67
40506070
100
Al oxideSi nitride
C/C( fibers)1
Al/Al oxide(sf)2
Al oxid/SiC(w)3
Al oxid/ZrO2(p)4Si nitr/SiC(w)5
Glass/SiC(w)6
Y2O3/ZrO2(p)4
Kcmetals
Kccomp
KccerKc
poly
incr
easi
ng
Based on data in Table B5,Callister 6e.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.
Fracture ToughnessFracture Toughness
[email protected] • ENGR-45_Lec-19_Failure-1.ppt25
Bruce Mayer, PE Engineering-45: Materials of Engineering
12
• Crack growth condition:
Y a
• Largest, most stressed cracks grow first
--Result 1: Max flaw size dictates design stress.
--Result 2: Design stress dictates max. flaw size.
design
Kc
Y amax amax
1
KcYdesign
2
K ≥ Kc
amax
no fracture
fracture
amax
no fracture
fracture
Design Against Crack GrowthDesign Against Crack Growth
(Y Unitless Geometry Factor)
[email protected] • ENGR-45_Lec-19_Failure-1.ppt26
Bruce Mayer, PE Engineering-45: Materials of Engineering
The Y-Parameter The Y-Parameter Y for Some Geometries and Loading
• B Material Base-depth (into Screen/Page)
[email protected] • ENGR-45_Lec-19_Failure-1.ppt27
Bruce Mayer, PE Engineering-45: Materials of Engineering
13
• Two designs to consider...Design A --largest physical flaw is 9 mm --failure stress = 112 MPa
Design B --use same material --largest physical flaw is 4 mm --failure stress = ?• Use...
maxaY
K Icc
• Key point: Y and KIc are the same in both designs. --Result:
c amax
A c amax
B
9 mm112 MPa 4 mm
Answer: c B 168MPa
• Reducing flaw size pays off!
• Material has KIc = 26 MPa-m0.5
Design Ex: Aircraft WingDesign Ex: Aircraft Wing
[email protected] • ENGR-45_Lec-19_Failure-1.ppt28
Bruce Mayer, PE Engineering-45: Materials of Engineering
Loading Rate Loading Rate Increased
Loading Rate• INcreases σy and TS
• DEcreases %EL
Reason• An increased rate
gives less time for dislocations to move past obstacles
Thus Material Deformation Can Be Different based on the DYNAMICS of the Load Application
y
y
TS
TSLarger d/dt
Smaller d/dt
[email protected] • ENGR-45_Lec-19_Failure-1.ppt29
Bruce Mayer, PE Engineering-45: Materials of Engineering
Temperature Effects Temperature Effects Increasing Temperature Increases %EL & Kc
• As Discussed Previously, Some Materials Exhibit a Ductile-to-Brittle Transition-Temperature (DBTT)
BCC metals (e.g., iron at T < 914C)
Imp
act
En
erg
y
Temperature
FCC metals (e.g., Cu, Ni)
High strength materials σy>E/150)
polymers
More Ductile Brittle
Ductile-to-brittle transition temperature
Charpy V-Notch(CVN) Impact
Test
[email protected] • ENGR-45_Lec-19_Failure-1.ppt30
Bruce Mayer, PE Engineering-45: Materials of Engineering
Design Criteria: Stay Above DBTT Design Criteria: Stay Above DBTT
Problem: DBTT ~ Room Temperature• Fabricate-OK; CRACK in Cold Water
• Pre-WWII: The Titanic • WWII: Liberty ships
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.)
[email protected] • ENGR-45_Lec-19_Failure-1.ppt31
Bruce Mayer, PE Engineering-45: Materials of Engineering
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