[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

[email protected]

Engineering 45

MaterialMaterialFailure Failure

(1)(1)



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



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



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:



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.



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



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.



Ductile vs. Brittle Tensile FailureDuctile vs. Brittle Tensile Failure Ductile Failure

“Cup-and-Cone” Fracture Surface

Brittle Failure

“Matted” Fracture Surface



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



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



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



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



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

=



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!



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



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.



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



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)



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



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



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



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



KKIIcc for Several Metals for Several Metals Higher Values

of KIc are Desired



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



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)



The Y-Parameter The Y-Parameter Y for Some Geometries and Loading

• B Material Base-depth (into Screen/Page)



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



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



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



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.)



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[email protected] engr-45_lec-19_failure-1.ppt 1 bruce mayer, pe engineering-45: materials of...

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