ISSUES TO ADDRESS...
• Stress and strain: What are they and why are they used instead of load and deformation?
• Elastic behavior: When loads are small, how much deformation occurs? What materials deform least?
• Plastic behavior: At what point do dislocations
cause permanent deformation? What materials are most resistant to permanent deformation?
• Toughness and ductility: What are they and how do we measure them?
CHAPTER 6:
Mechanical properties
Chapter 6-
F δ
bonds stretch
return to initial
2
1. Initial 2. Small load 3. Unload
Elastic means reversible!
F
δ
Linear- elastic
Non-Linear- elastic
Elastic deformation
1. Initial 2. Small load 3. Unload
Plastic means permanent!
F
δ
linear elastic
linear elastic
δ plastic
planes still
sheared
F
δ elastic + plastic bonds
stretch
& planes shear
δ plastic
Plastic deformation (metals)
Chapter 6- 4
• Tensile stress, σ: • Shear stress, τ:
Area, A
Ft Ft
σ = F t A o
original area before loading
Area, A
Ft Ft
Fs F
F Fs τ = F s
A o
Stress has units:
N/m 2 or lb/in 2
Engineering stress
• Simple tension: cable
o
σ = F A
• Simple shear: drive shaft
Ao = cross sectional Area (when unloaded)
F F
σ σ
o
τ = Fs A
τ
Note: τ = M/A c R here.
Ski lift
(photo courtesy P.M. Anderson)Common states of stress
M
M A o
2R
A c Fs
Chapter 6-
Canyon Bridge, Los Alamos, NM
• Simple compression:
6
A o
Balanced Rock, Arches National Park
o
σ = F A
Note: compressive structure member (σ < 0 here).
(photo courtesy P.M. Anderson)
(photo courtesy P.M. Anderson)
Other common stress states (1)
• Bi-axial tension: • Hydrostatic compression:
Fish under water Pressurized tank
σ z > 0 σθ > 0
(photo courtesy P.M. Anderson)
σ h < 0
(photo courtesy P.M. Anderson)
Other common stress states (2)
Chapter 6- 8
• Tensile strain: • Lateral strain:
• Shear strain:
θ/2
π/2
π/2 - θ
θ/2
δ/2
δ/2 δ L /2 δ L /2
L o w o
ε = δ
L o ε L =−
δ L w o
γ = tan θ Strain is always dimensionless.
Engineering strain
• Typical tensile specimen
• Other types of tests:
--compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes,
shafts.
gauge length
(portion of sample with reduced cross section)
=
• Typical tensile test machine
load cell
extensometer specimen
moving cross head
Adapted from Fig. 6.2, Callister 6e.
Adapted from Fig. 6.3, Callister 6e.
(Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.)
Stress-strain testing
Chapter 6-
• Modulus of Elasticity, E:
(also known as Young's modulus)
10
• Hooke's Law:
σ = E ε
• Poisson's ratio, ν:
metals: ν ~ 0.33 ceramics: ~0.25 polymers: ~0.40
ν = − ε ε L
ε L
ε 1 -ν
F
F
simple tension test
σ
Linear- elastic
1 E
ε
Units:
E: [GPa] or [psi]
ν: dimensionless
Linear elastic properties
• Elastic Shear modulus, G:
τ 1
G τ = G γ γ
• Elastic Bulk modulus, K:
P= - K ΔV Vo
P
ΔV -K 1 Vo
• Special relations for isotropic materials:
P
P P
M
M
G = E
2(1 + ν) K = E
3(1 − 2 ν)
simple torsion test
pressure test: Init.
vol =V o . Vol chg.
= ΔV
Other elastic properties
Chapter 6- 12 0.2
8
0.6 1
Magnesium, Aluminum Platinum Silver, Gold Tantalum Zinc, Ti Steel, Ni Molybdenum
Graphite Si crystal
Glass -soda
Concrete Si nitride Al oxide
PC
Wood( grain) AFRE( fibers) * CFRE*
GFRE*
Glass fibers only Carbon fibers only
Aramid fibers only
Epoxy only
0.4 0.8 2 4 6 10 20 40 60 10 080 200 600 10 00800 1200
400
Tin Cu alloys Tungsten
<100>
<111>
Si carbide Diamond
PTFE HDPE
LDPE PP Polyester
PS PET
CFRE( fibers) * GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
Metals Alloys
Graphite Ceramics Semicond
Polymers Composites /fibers
E(GPa)
Eceramics
> Emetals
>> Epolymers
10 9 Pa
Based on data in Table B2, Callister 6e.
Composite data based on reinforced epoxy with 60 vol%
of aligned
carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers.
Young’s moduli: comparison
• Simple tension:
δ = FL o EA o
δ L = − ν Fw o EA o
δ/2
δ/2 δ L /2 δ L /2
L o w o
F
Ao
• Simple torsion:
M=moment
α =angle of twist
2r o
Lo
α = 2ML o π r o 4 G
• Material, geometric, and loading parameters all contribute to deflection.
• Larger elastic moduli minimize elastic deflection.
Useful linear elastic relations
Chapter 6- 14
• Simple tension test:
tensile stress, σ
engineering strain, ε
(at lower temperatures, T < T melt /3)
Elastic initially
Elastic+Plastic at larger stress
permanent (plastic) after load is removed
ε p
p lastic strain
Plastic (permanent) deformation
• Stress at which noticeable plastic deformation has occurred.
when ε p = 0.002
tensile stress, σ
engineering strain, ε
σ y
ε p = 0.002
Yield strength, σ y
Chapter 6- 16 Graphite/
Ceramics/
Semicond Metals/
Alloys
Composites/
fibers Polymers
Yield strength, σ y (MPa)
PVC
Hard to measure, since in tension, fracture usually occurs before yield.
Nylon 6,6
LDPE
70
20 40 60 50 100
10 30 200 300 400 500600 700 10 00 2000
Tin (pure) Al (6061)a Al (6061)ag
Cu (71500)hr Ta (pure) Ti (pure) a Steel (1020)hr Steel (1020)cd Steel (4140)a Steel (4140)qt
Ti (5Al-2.5Sn)a W (pure) Mo (pure) Cu (71500)cw
Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield.
HDPE PP
humid dry
PC PET
¨
Room T values
σ y(ceramics)
>>σ y(metals)
>> σ y(polymers)
Based on data in Table B4, Callister 6e.
a = annealed hr = hot rolled ag = aged
cd = cold drawn cw = cold worked
qt = quenched & tempered
Yield strength: comparison
• Maximum possible engineering stress in tension.
• Metals: occurs when noticeable necking starts.
• Ceramics: occurs when crack propagation starts.
• Polymers: occurs when polymer backbones are aligned and about to break.
Adapted from Fig. 6.11, Callister 6e.
Tensile strength, TS
strain
engineering stress
TS
Typical response of a metal
Chapter 6- 18
Room T values
Si crystal
<100>
Graphite/
Ceramics/
Semicond Metals/
Alloys
Composites/
fibers Polymers
Tensile strength, TS (MPa)
PVC Nylon 6,6
10 100 200 300 10 00
Al (6061)a Al (6061)ag Cu (71500)hr
Ta (pure) Ti (pure) a Steel (1020)
Steel (4140)a Steel (4140)qt
Ti (5Al-2.5Sn)a W (pure) Cu (71500)cw
LDPE PP
PC PET
20 3040 2000 3000 5000
Graphite Al oxide
Concrete Diamond
Glass-soda Si nitride
HDPE
wood ( fiber) wood(|| fiber)
1
GFRE(|| fiber)
GFRE( fiber) CFRE(|| fiber)
CFRE( fiber) AFRE(|| fiber)
AFRE( fiber) E-glass fib
C fibers
Aramid fib
TS(ceram)
~TS (met)
~ TS(comp)
>> TS(poly)
Based on data in Table B4, Callister 6e.
a = annealed hr = hot rolled ag = aged
cd = cold drawn cw = cold worked
qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol%
fibers.
Tensile strength: comparison
• Plastic tensile strain at failure:
Engineering tensile strain, ε Engineering
tensile stress, σ
smaller %EL
(brittle if %EL<5%)
larg er %EL (ductile if
%EL>5%)
• Another ductility measure: %AR = A o − A f
A o x100
• Note: %AR and %EL are often comparable.
--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck.
Lo Ao Lf
Af
%EL = L f − L o
L o x100
Adapted from Fig. 6.13, Callister 6e.
Ductility, %EL
Chapter 6-
• Energy to break a unit volume of material
• Approximate by the area under the stress-strain curve.
20
smaller toughness- unreinforced
polymers
Engineering tensile strain, ε Engineering
tensile stress, σ
smaller toughness (ceramics)
larg er toughness (metals, PMCs)
Toughness
Resilience
σ y
Resilience is the capacity to absorb energy in the elastic region
Modulus of resilience is the total elastic strain energy per unit volume (Area under elastic portion of σ vs. ε)
Modulus of resilience (this area)
( )
U E
E d E
E d E d
E U
y r
r
y y
y
2
1
2
0 0
0
σ
σ σ σ σ
ε ε
σ σ
σ
=
=
=
= ∫ ∫ ∫
Resilient materials are used in spring applications. They have high yield stress and low modulus of elasticity.
Strain, ε
ε y
Stress, σ
, J/m
3Chapter 6-
Elastic properties of spring mtls
Material σ
yProp limit E Recov. Normalized (ksi) (ksi) 10
3ksi strain % Mod. of resil.
Ti-55Ni 30 27 10 1.00 1
17-7PH 200 180 29 0.62 2.2
MP55N-Co 225 203 33.6 0.6 2.4
5160 250 225 30 0.75 3.3
Ti-6Al-4V 120 108 16.5 0.65 1.4
Beta C Ann. 120 108 13.0 0.83 1.8
Beta C + CW 170 160 13.0 1.18 3.6
Beta C + CW+ Aged 210 185 15.5 1.22 4.6
• Resistance to permanently indenting the surface.
• Large hardness means:
--resistance to local plastic deformation or cracking in compression.
--better wear properties.
e.g., 10mm sphere (Brinell Hardness)
apply known force
(1 to 1000g) measure size of indent after removing load
d
D
Smaller indents mean larger hardness.
increasing hardness
most plastics
brasses Al alloys
easy to machine
steels file hard
cutting tools
nitrided
steels diamond
Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957.)
Hardness
Chapter 6-
• An increase in σ y due to plastic deformation.
• Curve fit to the stress-strain response:
22
σ
ε
large hardening small hardening
u n lo a d re
lo a d
σ y
0
σ y
1
σ T = C ( ) ε T n
“true” stress (F/A) “true” strain: ln(L/L o)
Strain hardening exponent:
n= 0.15 (some steels) to n= 0.5 (some copper)
Strain hardening
• Design uncertainties mean we do not push the limit.
• Factor of safety, N
σ working = σ y N
Often N is between 1.2 and 4
• Ex: Calculate a diameter, d, to ensure that yield does
not occur in the 1045 carbon steel rod below when subjected to a load of 200, 000N. Use a factor of safety of 5.
1045 plain
carbon steel:
σ y=310MPa TS=565MPa
F = 220,000N
d
σ working = σ y Lo N
220, 000N π ⎛ d 2 / 4
⎝ ⎜ ⎞
⎠ ⎟ 5
Design or safety factors
Chapter 6-
• Stress and strain: These are size-independent
measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often
shows a linear relation between stress and strain.
To minimize deformation, select a material with a large elastic modulus (E or G).
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive) uniaxial stress reaches σ y .
• Toughness: The energy needed to break a unit volume of material.
• Resilience: Energy absorbed during elastic deformation
• Ductility: The plastic strain at failure.
24
Summary
Reading: Chapter 6.1-12
Core Problems: Chapter 6, Problems 4, 8, 25, 29, 46
Self-help Problems: Review Example problems 6.2, 6.3, 6.4, 6.4, 6.5
ANNOUNCEMENTS
Course Title : Material Science Course Number : EMEC 2430
Credits : 4
Dr. M Shaaban Hussain
Unit – IV : Mechanical Failure, Tensile Test, Fatigue Test, Creep Test, Environmental Effect on basic Engineering Materials.
Books:
1. William D. Callister, Jr.; Materials Science &
Engineering: An Introduction.
2. Gupta, K.M.; Materials Science & Engineering
Failure
• The failure of engineering materials is almost always an undesirable event for several reasons; these include putting human lives in jeopardy, causing economic losses, and interfering with the availability of products and services.
• Even though the causes of failure and the behavior of materials may be known, prevention of failures is difficult to guarantee.
• The usual causes are improper materials selection and processing and inadequate design of the component or its misuse.
• Also, damage can occur to structural parts during
service, and regular inspection and repair or
replacement are critical to safe design. It is the
responsibility of the engineer to anticipate and plan for
possible failure and, in the event that failure does
occur, to assess its cause and then take appropriate
preventive measures against future incidents.
Mechanical Properties
• Three factors that should be considered in designing laboratory tests to assess the mechanical characteristics of materials for service use are:
• the nature of the applied load (i.e., tension, compression, shear),
• load duration, and
• environmental conditions.
Fracture
• Simple fracture is the separation of a body into two or more pieces in response to an imposed stress that is static (i.e., constant or slowly changing with time) and at temperatures that are low relative to the melting temperature of the material.
• Fracture can also occur from fatigue (when cyclic stresses are imposed) and creep (time-dependent deformation, normally at elevated temperatures)
• Although applied stresses may be tensile, compressive, shear, or torsional (or combinations of
•
For metals, two fracture modes are possible:
ductileand
brittle.Classification is based on the ability of a material to experience plastic deformation.
•
Ductile metals typically exhibit substantial plastic deformation with high energy absorption before fracture.
However, there is normally little or no plastic deformation with low energy absorption accompanying a brittle fracture.
•
Any fracture process involves two steps—crack formation and propagation—in response to an imposed stress.
•
The mode of fracture is highly dependent on the mechanism of crack propagation.
•
Ductile fracture is characterized by extensive plastic
• Furthermore, the process proceeds relatively slowly as the crack length is extended. Such a crack is often said to be stable—that is, it resists any further extension unless there is an increase in the applied stress.
• In addition, there typically is evidence of appreciable gross deformation at the fracture surfaces (e.g., twisting and tearing).
• However, for brittle fracture, cracks may spread extremely rapidly, with very little accompanying plastic deformation
• Such cracks may be said to be unstable, and crack propagation, once started, continues spontaneously without an increase in magnitude of the applied stress.
•
Ductile fracture is almost always preferred to brittle fracture for two reasons:
•
First, brittle fracture occurs suddenly and catastrophically without any warning; this is a consequence of the spontaneous and rapid crack propagation.
•
However, for ductile fracture, the presence of plastic deformation gives warning that failure is imminent, allowing preventive measures to be taken.
•
Second, more strain energy is required to induce ductile fracture in as much as these materials are generally tougher.
•
Under the action of an applied tensile stress, many metal alloys are ductile, whereas ceramics are typically brittle, and polymers may exhibit a range of behaviors.
DUCTILE FRACTURE
• Ductile fracture surfaces have distinctive features on both macroscopic and microscopic levels.
• Figure shows schematic representations for two characteristic macroscopic fracture profiles.
• The configuration shown in Figure (a) is found for extremely soft metals, such as pure gold and lead at room temperature, and other metals, polymers, and inorganic glasses at elevated temperatures. These highly ductile materials neck down to a point fracture, showing virtually 100% reduction in area.
• The most common type of tensile fracture profile for ductile metals is that represented in Figure (b), where fracture is
preceded by only a moderate amount of necking. Figure: (a) Highly ductile fracture in which the specimen necks down to a point.
(b) Moderately ductile fracture after some necking. (c) Brittle fracture without any plastic deformation.
Mechanism of Fracture (Ductile)
• The fracture process normally occurs in several stages . First, after necking begins, small cavities, or microvoids, form in the interior of the cross section, as indicated in Figure.
• Next, as deformation continues, these microvoids enlarge, come together, and coalesce to form an elliptical crack, which has its long axis perpendicular to the stress direction. The crack continues to grow in a direction parallel to its major axis by this microvoid coalescence process (refer Figure).
• Finally, fracture ensues by the rapid propagation of a crack around the outer perimeter of the neck by shear deformation at an angle of about 45 with the tensile axis—the angle at which the shear stress is a maximum. Sometimes a fracture having this characteristic surface contour is termed a cup-and- cone fracture because one of the mating surfaces is in the form of a cup and the other like a cone.
Figure: Stages in the cup-and-cone fracture. (a) Initial necking. (b) Small cavity formation. (c)
Crack Initiation & Propagation
• The process of fatigue failure is characterized by three distinct steps:
• (1) crack initiation, in which a small crack forms at some point of high stress concentration;
• (2) crack propagation, during which this crack advances incrementally with each stress cycle; and
• (3) final failure, which occurs very rapidly once the
advancing crack has reached a critical size.
Mechanism of Fracture (Brittle)
• Brittle fracture takes place without any appreciable deformation and by rapid crack propagation. The direction of crack motion is very nearly perpendicular to the direction of the applied tensile stress and yields a relatively flat fracture surface, as shown in earlier Figure.
• Fracture surfaces of materials that fail in a brittle manner have distinctive patterns; any signs of gross plastic deformation are absent.
• For most brittle crystalline materials, crack propagation
• corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes;
such a process is termed cleavage.
• This type of fracture is said to be transgranular (or transcrystalline) because the fracture cracks pass through the grains. Macroscopically, the fracture surface may have a grainy or faceted texture as a result of changes in orientation of the cleavage planes from grain to grain.
• In some alloys, crack propagation is along grain boundaries; this fracture is termed intergranular.
Fatigue
• Fatigue
is a form of failure that occurs in structures subjected to dynamic and fluctuating stresses (e.g., bridges, aircraft, machine components).
•
Under these circumstances, it is possible for failure to occur at a stress level considerably lower than the tensile or yield strength for a static load. The term
fatigueis used because this type of failure normally occurs after a lengthy period of repeated stress or strain cycling.
•
Fatigue is important in as much as it is the single largest cause of failure in metals, estimated to be involved in approximately 90% of all metallic failures; polymers and ceramics (except for glasses) are also susceptible to this type of failure.
• Furthermore, fatigue is catastrophic and insidious, occurring very suddenly and without warning. Fatigue failure is brittle-like in nature even in normally ductile metals in that there is very little, if any, gross plastic deformation associated with failure.
• The process occurs by the initiation and propagation of cracks, and typically the fracture surface is perpendicular to the direction of an applied tensile stress.
• The applied stress may be axial (tension–compression), flexural (bending), or torsional (twisting) in nature. In general, three different fluctuating stress–time modes are possible.
THE S–N CURVE
• As with other mechanical characteristics, the fatigue properties of materials can be determined from laboratory simulation tests.
• A test apparatus should be designed to duplicate as nearly as possible the service stress conditions (stress level, time frequency, stress pattern, etc.).
• The most common type of test conducted in a laboratory setting employs a rotating–bending beam:
alternating tension and compression stresses of equal magnitude are imposed on the specimen as it is simultaneously bent and rotated.
• In this case, the stress cycle is reversed—that is, R=-1. Schematic diagrams of the apparatus and test specimen commonly used for this type of fatigue testing as shown in Figures a and b, respectively.
• From Figure (a), during rotation, the lower surface of the specimen is subjected to a tensile (i.e., positive) stress, whereas the upper surface experiences compression (i.e., negative) stress.
Figure :For rotating–bending fatigue tests, schematic diagrams of (a) a testing apparatus, and (b) a test
• A series of tests is commenced by subjecting a specimen to stress cycling at a relatively large maximum stress (σ
�), usually on the order of two- thirds of the static tensile strength; number of cycles to failure is counted and recorded.
• This procedure is repeated on other specimens at
progressively decreasing maximum stress levels. Data
are plotted as stress S versus the logarithm of the
number N of cycles to failure for each of the
specimens. The S parameter is normally taken as either
maximum stress ( σ
�) or stress amplitude ( σ
�)
(Figures a and b).
• Two distinct types of S–N behavior are observed and are represented schematically in Figures. As these plots indicate, the higher the magnitude of the stress, the smaller the number of cycles the material is capable of sustaining before failure.
• For some ferrous (iron-base) and titanium alloys, the S–
N curve (see Figure a) becomes horizontal at higher N values; there is a limiting stress level, called the fatigue limit (also sometimes called the endurance limit), below which fatigue failure will not occur. This fatigue limit represents the largest value of fluctuating stress that will not cause failure for essentially an infinite number of cycles.
Figure: Stress amplitude (S) versus logarithm of the number of cycles to fatigue failure (N) for (a) a material that displays a fatigue limit and (b) a material that does not display a fatigue limit
Figure: Maximum stress (S) versus logarithm of the number of cycles to fatigue failure (N) for seven metal alloys. Curves were generated using rotating–bending and reversed-cycle tests.
Environmental Effects
• Environmental factors may also affect the fatigue behavior of materials. A few brief comments will be given relative to two types of environment-assisted fatigue failure: thermal fatigue and corrosion fatigue.
• Thermal fatigue is normally induced at elevated temperatures by fluctuating thermal stresses;
mechanical stresses from an external source need
not be present. The origin of these thermal stresses
is the restraint to the dimensional expansion and/or
contraction that would normally occur in a structural
member with variations in temperature.
• Thermal stresses do not arise if this mechanical restraint is absent. Therefore, one obvious way to prevent this type of fatigue is to eliminate, or at least reduce, the restraint source, thus allowing unhindered dimensional changes with temperature variations, or to choose materials with appropriate physical properties.
• Failure that occurs by the simultaneous action of a cyclic stress and chemical attack is termed corrosion fatigue.
• Corrosive environments have a deleterious influence and produce shorter fatigue lives. Even normal ambient atmosphere affects the fatigue behavior of some materials. Small pits may form as a result of chemical reactions between the environment and the material, which may serve as points of stress concentration and therefore as crack nucleation sites.
• In addition, the crack propagation rate is enhanced as a result of the corrosive environment. The nature of the stress cycles influences the fatigue behavior; for example, lowering the load application frequency leads to longer periods during which the opened crack is in contact with the environment and to a reduction in the fatigue life.
• Several approaches to corrosion fatigue prevention exist. We can take measures to reduce the rate of corrosion by some of the techniques, for example, apply protective surface coatings, select a more corrosion-resistant material, and reduce the corrosiveness of the environment.
• On the other hand, it might be advisable to take actions to minimize the probability of normal fatigue failure, as outlined previously—for example, reduce the applied
tensile stress level and impose residual compressive
stresses on the surface of the member.•
Measures that may be taken to extend fatigue life include the following:
•
Reducing the mean stress level
•
Eliminating sharp surface discontinuities
•
Improving the surface finish by polishing
•
Imposing surface residual compressive stresses by shot peening
•
Case hardening by using a carburizing or nitriding process
Creep
• Creep
is
defined as the time-dependent and permanentdeformation of materials when subjected to a constant load or stress, creep is normally an undesirable phenomenon and is often the limiting factor in the lifetime of a part.
•
Materials are often placed in service at elevated temperatures and exposed to static mechanical stresses (e.g., turbine rotors in jet engines and steam generators that experience centrifugal stresses; high-pressure steam lines).
•
It is observed in all materials types; for metals, it
•
about 0.4Tm, where
Tmis the absolute melting
temperature. Amorphous polymers, which include plastics and rubbers, are especially sensitive to creep deformation.•
A typical creep test consists of subjecting a specimen to a constant load or stress while maintaining the temperature constant; deformation or strain is measured and plotted as a function of elapsed time. Most tests are the constant-load type, which yield information of an engineering nature; constant-stress tests are employed to provide a better understanding of the mechanisms of creep.
Creep Behaviour
• A typical creep curve (strain versus time) normally exhibits three distinct regions: transient (or primary), steady-state (or secondary), and tertiary., each of which has its own distinctive strain–time feature.
• Primary or transient creep occurs first, typified by a
continuously decreasing creep rate—that is, the slope of
the curve decreases with time. This suggests that the material is experiencing an increase in creep resistance or strain hardening deformation becomes more difficult as thematerial is strained.
• Forsecondary creep,sometimes termedsteady-state creep, the rate is constant—that is, the plot becomes linear. This is often the stage of creep that is of the longest duration. The
constancy of creep rate is explained on the basis of a
• balance between the competing processes of strain hardening and recovery, recovery being the process by which a material becomes softer and retains its ability to
experience deformation.
• Finally, for tertiary creep, there is an acceleration of the rate and ultimate failure. This failure is frequently termed rupture and results from microstructural and/or
metallurgical changes—for example, grain boundary
separation, and the formation of internal cracks, cavities, and voids. Also, for tensile loads, a neck may form at some point within the deformation region. These all lead to adecrease in the effective cross-sectional area and an
increase in strain rate.• Important design parameters available from such a plot include the steady-state creep rate (slope of the linear
region) and rupture lifetime.
Figure: Typical creep curve of strain versus time at constant load and constant elevated temperature. The minimum creep rate Δe/Δt is the slope of the linear segment in the secondary region. Rupture lifetime tris the total time to rupture.
• For metallic materials, most creep tests are conducted in uniaxial tension using a specimen having the same geometry as for tensile tests. However, uniaxial compression tests are more appropriate for brittle materials; these provide a better measure of the intrinsic creep properties because there is no stress amplification and crack propagation, as with tensile loads. Compressive test specimens are usually right cylinders or parallelepipeds having length-to-diameter ratios ranging from about 2 to 4.
• For most materials, creep properties are virtually independent of loading direction. Possibly the most
important parameter from a creep test is the slope of the
secondary portion of the creep curve; this is often called the minimum or steady-state creep rate. It is the engineering design parameter that is considered for long-life applications, such as a nuclear power plant component.
• The results of creep rupture tests are most commonly presented as the logarithm of stress versus the logarithm of rupture lifetime. Next Figure is one such plot for an S-590 alloy in which a set of linear relationships can be seen to exist at each temperature.
• For some alloys and over relatively large stress ranges, nonlinearity in these curves is observed.
• Empirical relationships have been developed in which the steady-state creep rate as a function of stress and temperature is expressed.
• Both temperature and applied stress level influence creep behavior. Increasing either of these parameters produces the following effects:
An increase in the instantaneous initial deformation An increase in the steady-state creep rate
A decrease in the rupture lifetime
•
Metal alloys that are especially resistant to creep have
high elastic moduli and melting temperatures; these
include the super alloys, the stainless steels, and the
refractory metals. Various processing techniques are
employed to improve the creep properties of these
Chapter 8-
ISSUES TO ADDRESS...
• How do flaws in a material initiate failure?
• How is fracture resistance quantified; how do different material classes compare?
• How do we estimate the stress to fracture?
1
• How do loading rate, loading history, and temperature affect the failure stress?
Ship-cyclic loading from waves.
Computer chip-cyclic thermal loading.
Hip implant-cyclic loading from walking.
Adapted from Fig. 8.0, Callister 6e.(Fig.
8.0 is by Neil Boenzi, The New York Times.)
Adapted from Fig. 18.11W(b), Callister 6e.
(Fig. 18.11W(b) is courtesy of National Semiconductor Corporation.)
Adapted from Fig.
17.19(b), Callister 6e.
CHAPTER 8:
Mechanical failure
Very Ductile
Moderately
Ductile Brittle Fracture
behavior:
Large Moderate
%AR or %EL : Small
• Ductile fracture is desirable!
• Classification:
Ductile:
warning before fracture
Brittle:
No warning
Adapted from Fig. 8.1, Callister 6e.
Ductile vs brittle failure
Chapter 8- 3
• Ductile failure:
--one piece
--large deformation
• Brittle failure:
--many pieces
--small 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.
Ex: Failure of a pipe
• Evolution to failure:
necking void
nucleation
void growth
and linkage shearing
at surface fracture
σ
• Resulting fracture surfaces
(steel)
50 μm
particles
serve as void nucleation sites.
50 μm
100 μm
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.
Fracture surface of tire cord wire loaded in tension. Courtesy of F.
Roehrig, CC Technologies, Dublin, OH. Used with permission.
Cup
&
45° Cone angle
Moderately ductile failure
Chapter 8- 5
• Intergranular
(between grains)
• Intragranular
(within 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,
"Defor-mation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p.
303, John Wiley and Sons, Inc., 1996.
3μm
4 mm 160μm
1 mm
(Orig. source: K. Friedrick, Fracture 1977, Vol.
3, ICF4, Waterloo, CA, 1977, p. 1119.)
Brittle fracture surfaces
• Stress-strain behavior (Room T):
σ
ε
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic typical strengthened metal typical polymer
TS << TS engineering materials
perfect materials
• DaVinci (500 yrs ago!) observed...
--the longer the wire, the smaller the load to fail it.
• Reasons:
--flaws cause premature failure.
--Larger samples are more flawed!
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 materials
Chapter 8- 7
• Elliptical hole in a plate:
• Stress distrib. in front of a hole:
• Stress conc. factor:
BAD! Kt>>3
NOT SO
BAD Kt=3
σ max
ρ t
≈ σ o ⎛ 2 a + 1
⎝ ⎜ ⎞
⎠ ⎟ ρ t
σ σ o
2a
K t = σ max / σ o
• Large K t promotes failure:
Flaws are stress concentrators!
• Avoid sharp corners!
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 σ σ max
o
=
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.)
Engineering fracture design
r , fillet radius
w h
σ o
σ max
Chapter 8-
• ρ t at a crack tip is very
small!
9
σ
• Result: crack tip stress is very large.
• Crack propagates when:
the tip stress is large
enough to make crack unstable (?):
When does a crack propagate?
σ
aa π a
2t t
2
Strain energy U s = U o + V o ( ) ( )
σ
22E
σ
22E π a
2t
- 2
Energy of a crack U crack = 2γat volume Total energy = Strain energy +
Energy of the crack Crack will propagate if energy decreases, i.e. crack length is greater than a crit
a crit energy
Crack length
2 π a
critWhen does a crack propagate?
2 γ E
σ >
2 π a
σ > K IC
Chapter 8- 10
• Condition for crack propagation:
• Values of K for some standard loads & geometries:
σ
2a 2a
σ
aa
K = σ πa K = 1.1 σ πa
K ≥ K c
Stress Intensity Factor:
--Depends on load &
geometry.
Fracture Toughness:
--Depends on the material, temperature, environment, &
rate of loading.
units of K : MPa m or ksi in
Adapted from Fig. 8.8, Callister 6e.
Geometry, load, & material
Graphite/
Ceramics/
Semicond Metals/
Alloys Composites/
fibers Polymers
5
K Ic (MPa · m 0.5 )
1
Mg alloys Al alloys
Ti alloys Steels
Si crystal Glass -soda Concrete
Si carbide
PC
Glass6 0.7
2 4 3 10 20 30
<100>
<111>
Diamond
PVC PP
Polyester PS
PET
C-C(|| fibers) 1
0.6 67 40 5060 70 100
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 Y2O3/ZrO2(p)4
Kc metals Kc comp Kc cer ≈ Kc poly
increasing
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 toughness
Chapter 8- 12
• Crack growth condition:
Y σ π a
• Largest, most stressed cracks grow first!
--Result 1: Max flaw size dictates design stress.
--Result 2: Design stress dictates max. flaw size.
σ design < K c
Y πa max a max <
1 π
K c Yσ design
⎛
⎝ ⎜
⎜
⎞
⎠ ⎟
⎟
2
K ≥ K c
amax
σ
no
fracture
fracture
amax
no σ
fracture
fracture
Design against crack growth
• 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 = ?
• Use...
σ c = K c
Y πa max
• Key point: Y and K c are the same in both designs.
--Result:
σ c a max
( 9 mm ) A = σ ( c a max ) B
112 MPa 4 mm
Answer: ( ) σ c B = 168MPa
• Reducing flaw size pays off!
• Material has K c = 26 MPa-m 0.5
Design example: Aircraft wing
Chapter 8- 14
• Increased loading rate...
--increases σ y and TS --decreases %EL
• Why? An increased rate gives less time for disl. to
move past obstacles.
initial height final height
sample
σ
ε σ y
σ y
TS
TS larger ε
small er ε
(Charpy)
• Impact loading:
--severe testing case --more brittle
--smaller toughness
Adapted from Fig. 8.11(a) and (b), Callister 6e. (Fig. 8.11(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.)
Loading rate
BCC metals (e.g., iron at T < 914C)
Impact Energy
Temperature
• Increasing temperature...
--increases %EL and K c
• Ductile-to-brittle transition temperature (DBTT)...
FCC metals (e.g., Cu, Ni )
High strength materials ( σ y>E/150) polymers
More Ductile Brittle
Ductile-to-brittle
transition temperature
Adapted from C. Barrett, W. Nix, and A.Tetelman, The Principles
of Engineering Materials, Fig. 6-21, p.
220, Prentice-Hall, 1973.
Electronically reproduced by
permission of Pearson Education, Inc., Upper Saddle River, New
Jersey.
Temperature
Chapter 8- 16
• Pre-WWII: The Titanic • WWII: Liberty ships
• Problem: Used a type of steel with a DBTT ~ Room temp.
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.)
Design strategy:
stay above the DBTT!
• Fatigue = failure under cyclic stress.
tension on bottom compression on top
counter
motor
flex coupling
bearing bearing
specimen
• Stress varies with time.
--key parameters are S and σ m σ max
σ min
σ
time
σ m S
• Key points: Fatigue...
--can cause part failure, even though σ max < σ c .
--causes ~ 90% of mechanical engineering failures.
Adapted from Fig. 8.16, Callister 6e. (Fig. 8.16 is from Materials Science in Engineering, 4/E by Carl.
A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.)
Fatigue
Chapter 8- 18
• Fatigue limit, S fat :
--no fatigue if S < S fat
• Sometimes, the
fatigue limit is zero!
Sfat
case for steel (typ.)
N = Cycles to failure
103 105 107 109
unsafe
safe
S = stress amplitude
case for Al (typ.)
N = Cycles to failure
103 105 107 109
unsafe
safe
S = stress amplitude
Adapted from Fig.
8.17(a), Callister 6e.
Adapted from Fig.
8.17(b), Callister 6e.
Fatigue design parameters S-N curve
(Endurance limit)
Fatigue strength
Fatigue life
• Crack grows incrementally
da
dN = ΔK ( ) m typ. 1 to 6
~ ( ) Δσ a
increase in crack length per loading cycle
• Failed rotating shaft
--crack grew even though K max < K c
--crack grows faster if
• Δσ increases
• crack gets longer
• loading freq. increases.
crack origin
Adapted from
Fig. 8.19, Callister 6e.
(Fig. 8.19 is from D.J.
Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.)
Fatigue mechanism
Chapter 8-
Fatigue striations in Al
1. Impose a compressive surface stress
(to suppress surface cracks from growing)
--Method 1: shot peening
2. Remove stress
concentrators. bad
bad
better better
--Method 2: carburizing
C-rich gas put
surface into compression shot
Adapted from
Fig. 8.23, Callister 6e.
N = Cycles to failure
moderate tensile σ m larger tensile σ m S = stress amplitude
near zero or compressive σ m
Adapted from
Fig. 8.22, Callister 6e.
Improving fatigue life
Chapter 8-
time
elastic
primary secondary
tertiary
T < 0.4 Tm
INCREASING T
0
strain, ε
• Occurs at elevated temperature, T > 0.4 T melt
• Deformation changes with time.
21 Adapted from
Figs. 8.26 and 8.27, Callister 6e.
Creep
σ,ε σ
0 t
• Most of component life spent here.
• Strain rate is constant at a given T, σ
--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
for larger T, σ
10 20 40 100 200
Steady state creep rate (%/1000hr) 10-2 10-1 1
ε s Stress (MPa)
427C 538C
649C
Adapted from
Fig. 8.29, Callister 6e.
(Fig. 8.29 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.)
ε s = K 2 σ n exp − Q c RT
⎛
⎝ ⎜ ⎞
⎠ ⎟ .
Secondary creep
Chapter 8- 24
