1. Chapter 8: Mechanical Failure
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?
• 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.

2. Failure mechanisms Fracture Fatigue Creep Corrosion Buckling Melting
Thermal shock
Wear

3. 1. Fracture mechanisms Ductile fracture
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.
The applied stress may be tensile, compressive, shear, or torsional;
Ductile fracture
Occurs with plastic deformation
Brittle fracture
Little or no plastic deformation
Suddenly and catastrophic
Any fracture process involves two steps—crack formation and propagation—in response to an imposed stress

4. Ductile vs Brittle Failure
• Classification:
Very
Ductile
Moderately
Brittle
Fracture
behavior:
Large
Moderate
%AR or %EL
Small
Ductility is a function of temperature of the material, the strain rate, and the stress state. May be quantified in term of %AR or %EL
• Ductile
fracture is usually
desirable!
Ductile:
warning before fracture
More strain energy is required
Brittle: No warning

5. Example: Failure of a Pipe
• Ductile failure:
--one piece
--large deformation
• Brittle failure:
--many pieces
--small deformation

6. Moderately Ductile Failure
• Evolution to failure:( stages in the cup-cone fracture)
void
nucleation
void growth
and linkage
shearing
at surface
necking s
fracture
• Resulting
fracture
surfaces
(steel)
50 mm
particles
serve as void
nucleation
sites.
100 mm

7. Ductile vs. Brittle Failure
cup-and-cone fracture in aluminum
brittle fracture in a mild steel
Metal alloys are ductile
Ceramics are notably brittle
Polymers may exhibit both types of fracture.

8. Brittle Failure
Brittle fracture takes place without any appreciable deformation, and by rapid crack propagation.
Arrows indicate point at which failure originated

9. Brittle Fracture Surfaces
• Inter-granular
(the fracture cracks pass through the grains)
• Intra-granular
(crack propagation is along grain boundaries)
304 S. Steel (metal)
160 mm
4 mm
316 S. Steel (metal)
Al Oxide
(ceramic)
Polypropylene
(polymer)
3 mm
1 mm

10. Principles of fracture mechanics
This subject allows quantification of the relationships between material properties, stress level, the presence of crack-producing flaws, and crack propagation mechanisms.
stress concentration
Fracture toughness
Design using fracture mechanics
Impact fracture testing

11. Flaws are Stress Concentrators!
Stress Concentration
Flaws are Stress Concentrators!
Results from crack propagation
Griffith Crack
where t = radius of curvature
so = applied stress=F/A
sm = stress at crack tip t
Stress concentrated at crack tip
Flaws: are called stress raiser

12. Concentration of Stress at Crack Tip
Stress amplification is not restricted
to these microscopic defects; it may occur at macroscopic internal discontinuities (e.g., voids), at sharp corners, and at notches in large structures.
The effect of a stress raiser is more significant in brittle than in ductile materials. For a ductile material, plastic deformation ensues when the maximum stress exceeds the yield strength. This lead to a more uniform distribution of stress in the vicinity of the stress raiser. Such yielding and stress redistribution do not occur to any appreciable extent around flaws and discontinuities in brittle materials; therefore, essentially the theoretical stress concentration will result.

13. Engineering Fracture Design
• Avoid sharp corners! s
r/h
sharper fillet radius
increasing
w/h
0.5
1.0
1.5
2.0
2.5
Stress Conc. Factor, K t s
max o =
r ,
fillet
radius w h o s
max
It is a measure of the degree to which an external stress is amplified at
the tip of a crack.

14. Crack Propagation Cracks propagate due to sharpness of crack tip
A plastic material deforms at the tip, “blunting” 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
plastic

15. When Does a Crack Propagate?
Crack propagates if applied stress is above critical stress sc ( it is the stress required for crack propagation in a brittle materials)
where
E = modulus of elasticity
s = specific surface energy
a = one half length of internal crack
Kc = sc/s0
For ductile => replace gs by gs + gp
where gp is plastic deformation energy
i.e., sm > sc
or Kt > Kc

16. problem

17. Design Against Crack Growth
Relationship between critical stress for crack propagation (σc) to crack length (a)
- Is fracture toughness, a property that is a measure of a
material’s resistance to brittle fracture when a crack is present.
Y is a dimensionless parameter or function that depends on both
crack and specimen sizes and geometries, as well as the
manner of load application.( Y = 1 – 1.1)

18. Fracture Toughness ) (MPa · m K KIC - plane strain fracture toughness
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 6
0.7 2 4 3 10
<100>
<111>
Diamond
PVC PP
Polyester PS
PET
C-C
(|| fibers)
0.6 7
100
Al oxide
Si nitride
C/C
( fibers)
Al/Al oxide(sf)
Al oxid/SiC(w)
Al oxid/ZrO
(p)
Si nitr/SiC(w)
Glass/SiC(w) Y O
/ZrO
KIC - plane strain fracture toughness
Based on data in Table B5,
Callister 7e.
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
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/ /2, ORNL, 1992.
6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp

19. The modes of crack surface displacement
The three modes of crack surface displacement. (a) Mode I, opening or tensile mode; (b) mode II, sliding mode; and ( c) mode III, tearing mode.

20. Design Against Crack Growth
• Crack growth condition:
K ≥ Kc =
• Largest, most stressed cracks grow first!
--Result 1: Max. flaw size
dictates design stress. s
amax no
fracture
--Result 2: Design stress
dictates max. flaw size.
amax s no
fracture

21. Plane strain fracture toughness
Exist when specimen thickness is much greater than the crack dimensions, Kc
becomes independent of thickness; under these conditions a condition of plane strain exists. By plane strain we mean that when a load operates on a crack there is no strain component perpendicular to the front and back faces. The Kc value for this thick-specimen situation is known as the plane strain fracture toughness KIc
The plane strain fracture toughness KIc is a fundamental material property that depends on many factors, the most influential of which are temperature, strain rate, and microstructure. The magnitude of KIc diminishes with increasing strain rate and decreasing temperature. increases with reduction in grain size

22. Design Example: Aircraft Wing
• Material has Kc = 26 MPa-m0.5
• 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...
• Key point: Y and Kc are the same in both designs.
9 mm
112 MPa
4 mm
--Result:
Answer:
• Reducing flaw size pays off!

23. Loading Rate s sy e • Increased loading rate...
-- increases sy and TS
-- decreases %EL
• Why? An increased rate
gives less time for
dislocations to move past
obstacles. s e sy TS
larger
smaller

24. Impact Testing • Impact loading:
-- determine the fracture properties of
materials
-- determine DBTT or not for materials
(Charpy)
final height
initial height
(Izod)

25. Temperature
DBTT – is the material a ductile-to-brittle transition with decreasing temperature and, if so, the range of temperatures over which it occur
• Ductile-to-Brittle Transition Temperature (DBTT)...
FCC metals (e.g., Cu, Ni)
BCC metals (e.g., iron at T < 914°C)
polymers
Impact Energy
Brittle
More Ductile
High strength materials ( s y
> E/150)
Temperature
Ductile-to-brittle
transition temperature
For steel

26. Structures constructed from alloys that exhibit this ductile-to-brittle behavior should be used only at temperatures above the transition temperature, to avoid brittle and catastrophic failure. Classic examples of this type of failure occurred, with disastrous consequences, during World War II when a number of welded transport ships, away from combat, suddenly and precipitously split in half. The vessels were constructed of a steel alloy that possessed adequate ductility according to room-temperature tensile tests. The brittle fractures occurred at relatively low ambient temperatures, at about 4C (40F), in the vicinity of the transition temperature of the alloy. Each fracture crack originated at some point of stress concentration, probably a sharp corner or fabrication defect, and then propagated around the entire girth of the ship

27. Design Strategy: Stay Above The DBTT!
• Pre-WWII: The Titanic
• WWII: Liberty ships
• Problem: Used a type of steel with a DBTT ~ Room temp.

28. 2. Fatigue
• Fatigue = failure under dynamics and fluctuating stress(cyclic).
tension on bottom
compression on top
counter
motor
flex coupling
specimen
bearing s
max
min
time m S
• Stress varies with time.
-- key parameters are S, sm, and frequency
• Key points: Fatigue...
--can cause part failure, even though smax < sc.
--causes ~ 90% of mechanical engineering failures.

29. Mean stress
Range of stress
Stress amplitude
Stress ratio

30. Fatigue Design Parameters S-N curve
• Fatigue limit, Sfat:
--no fatigue if S < Sfat
Sfat
case for
steel
(typ.)
N = Cycles to failure 10 3 5 7 9
unsafe
safe
S = stress amplitude
• Sometimes, the
fatigue limit is zero!
case for Al
(typ.)
N = Cycles to failure 10 3 5 7 9
unsafe
safe
S = stress amplitude

31. The important parameters that characterize a material’s fatigue behavior are
fatigue limit: This fatigue limit represents the largest value of fluctuating stress that will not cause failure for essentially an infinite number of cycles(below which fatigue failure will not occur.( most nonferrous alloys (Al,Cu,…)don’t have FL
fatigue life Nf . It is the number of cycles to cause failure at a specified stress level, as taken from the S–N plot

32. Fatigue Mechanism
The process of fatigue failure is characterized by three distinct steps: (1) crack initiation, wherein 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.
Cracks associated with fatigue failure almost always initiate (or nucleate) on the surface of a component at some point of stress concentration. Crack nucleation sites include surface scratches, sharp fillets, keyways, threads, dents, and the like. In addition, cyclic loading can produce microscopic surface discontinuities resulting from dislocation slip steps which may also act as stress raisers, and therefore as crack initiation sites.

33. Fatigue Mechanism • Crack grows incrementally • Failed rotating shaft
typ. 1 to 6( constant)
increase in crack length per loading cycle
crack origin
• Failed rotating shaft
--crack grew even though
Kmax < Kc
--crack grows faster as
• Ds increases
• crack gets longer
• loading freq. increases.

34. Factors that affect fatigue life
Mean stress
Surface effects
Environmental effects

35. 1. Mean stress
The dependence of fatigue life on stress amplitude is represented on the S–N plot. increasing the mean stress level leads to a decrease in fatigue life

36. 2. Surface effect
For many common loading situations, the maximum stress within a component or structure occurs at its surface. consequently, most cracks leading to fatigue failure originate at surface positions, specifically at stress amplification sites
Design factor: Any notch or geometrical discontinuity can act as a stress raiser and fatigue crack initiation site; these design features include grooves, holes, keyways, threads and so on.
Surface treatment: 1. improving the surface finish by polishing will enhance fatigue life significantly 2. imposing residual compressive stresses within a thin outer surface layer
Case (layer)hardening: is a technique whereby both surface hardness and fatigue life are enhanced for steel alloys. This is accomplished by a carburizing or nitriding process whereby a component is exposed to a carbonaceous or nitrogenous atmosphere at an elevated temperature.

37. Environmental effects
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. The magnitude of a thermal stress developed by a temperature change T is dependent on the coefficient of thermal expansion l and the modulus of elasticity E according to
Influence of stress and temperature T on creep behavior.

38. Corrosion fatigue: Failure that occurs by the simultaneous action of a cyclic stress and chemical attack
Small pits may form as a result of chemical reactions between the environment and material, which serve as points of stress concentration, and therefore as crack nucleation sites.
Several approaches to corrosion fatigue prevention
exist:
- apply protective surface coatings,
- select a more corrosion resistant material
- reduce the corrosiveness of the environment.

39. Improving Fatigue Life
1. Impose a compressive
surface stress
(to suppress surface
cracks from growing)
N = Cycles to failure
moderate tensile s m
Larger tensile
S = stress amplitude
near zero or compressive
Increasing m
--Method 1: shot peening
put
surface
into
compression
shot
--Method 2: carburizing
C-rich gas
2. Remove stress
concentrators.
bad
better

40. 3. Creep
The time-dependent permanent deformation that occurs when material are subjected to a constant load or stress; for most materials it is important only at elevated temperatures.
For metals it becomes important only for temperatures greater than about 0.4Tm (Tm absolute melting temperature).

41. Creep Sample deformation at a constant stress (s) vs. time s s,et
Primary Creep: slope (creep rate) decreases with time.
Secondary Creep: steady-state i.e., constant slope.
Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate.

42. Creep • Occurs at elevated temperature, T > 0.4 Tm tertiary primary
secondary
elastic

44. Secondary Creep • Strain rate is constant at a given T, s
-- strain hardening is balanced by recovery
stress exponent (material constant)
activation energy for creep
(material constant)
strain rate
material const.
applied stress
With either increasing stress or temperature, the following will be noted:
the instantaneous strain at the time of stress application increases;
the steady-state creep rate is increased;
(3) the rupture lifetime is diminished.

45. Stress (logarithmic scale) versus steady-state creep rate
Stress (logarithmic scale) versus rupture lifetime (logarithmic
scale) for a low carbon–nickel alloy at three temperatures
• Strain rate
increases
for higher T, s 10 2 4 -2 -1 1
Steady state creep rate (%/1000hr) e s
Stress (MPa)
427°C
538 °C
649
Stress (logarithmic scale) versus steady-state creep rate
(logarithmic scale) for a low carbon–nickel alloy at three temperatures.

46. Creep Failure • Failure: along grain boundaries. • Time to rupture, tr
time to failure (rupture)
function of
applied stress
temperature
applied
stress
g.b. cavities
• Time to rupture, tr
• EX. Estimate rupture time
S-590 Iron, T = 800°C, s = 20 ksi
L(10 3
K-log hr)
Stress, ksi
100 10 1 12 20 24 28 16
data for
S-590 Iron
From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John Wiley and Sons, Inc., (Orig. source: Pergamon Press, Inc.)
1073K
Ans: tr = 233 hr
24x103 K-log hr

47. ALLOYS FOR HIGH-TEMPERATURE USE
There a several factors that affect the creep characteristics of metals. These include melting temperature, elastic modulus, and grain size. In general, the higher the melting temperature, the greater the elastic modulus, and the larger the grain size, the better is a material’s resistance to creep.
Stainless steels, the refractory metals and the superalloys are especially resilient to creep and are commonly employed in high-temperature service applications. The creep resistance of the cobalt and nickel superalloys is enhanced by solid-solution alloying, and also by the addition of a dispersed phase which is virtually insoluble in the matrix. In addition, advanced processing techniques have been utilized; one such technique is directional solidification, which produces either highly elongated grains or single-crystal

49. 4. Corrosion
Corrosion is breaking down! of essential properties in a material due to reactions with its surroundings. In the most common use of the word, this means a loss of an electron of metals reacting with water and oxygen
Weakening of iron due to oxidation of the iron atoms is a well-known example of electrochemical corrosion. This is commonly known as rust This type of damage usually affects metallic materials, and typically produces oxide(s) and/or salt(s) of the original metal

50. Rust, the most familiar example of corrosion
-- Most structural alloys corrode merely from exposure to moisture in the air, but the process can be strongly affected by exposure to certain substances. Corrosion can be concentrated locally to form a pit or crack, or it can extend across a wide area to produce general deterioration

51. Resistant to corrosion
Intrinsic chemistry:
The materials most resistant to corrosion are those for which corrosion is thermodynamically unfavorable. Any corrosion products of gold or platinum tend to decompose spontaneously into pure metal, which is why these elements can be found in metallic form on Earth, and is a large part of their intrinsic value
GOLD nuggets do not corrode, even on a geological time scale.

52. Passivation:
Given the right conditions, a thin film of corrosion products can form on a metal's surface spontaneously, acting as a barrier to further oxidation. When this layer stops growing at less than a micrometre thick under the conditions that a material will be used in, the phenomenon is known as passivation
Passivation in air and water is seen in such materials as aluminum, stainless steel, titanium, and silicon

53. surface treatment ( coating ):
Plating, painting, and the application of enamel are the most common anti-corrosion treatments. They work by providing a barrier of corrosion-resistant material between the damaging environment and the (often cheaper, tougher, and/or easier-to-process) structural material
Example: chromium on steel

54. 5. Buckling
In engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high compressive stresses, where the actual compressive stresses at failure are smaller than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as failure due to elastic instability

55. Buckling in columns
A column under a centric axial load exhibiting the characteristic deformation of buckling
The eccentricity of the axial force results in a bending moment acting on the beam element

56. Euler formula that gives the maximum axial load ( critical load) that column can carry without buckling
F = maximum or critical force (vertical load on column),
E = modulus of elasticity,
I = area moment of inertia,
l = unsupported length of column,
K = column effective length factor, whose value depends on the conditions of end support of the column, as follows.
For both ends pinned (hinged, free to rotate), K = 1.0.
For both ends fixed, K = 0.50.
For one end fixed and the other end pinned, K = 0.70.
For one end fixed and the other end free to move laterally, K = 2.0.

57. 6. Melting
Melting is a process that results in the phase change of a substance from a solid to a liquid. The internal energy of a solid substance is increased (typically by the application of heat) to a specific temperature (called the melting point) at which it changes to the liquid phase. An object that has melted completely is molten
The melting point of a substance is equal to its freezing point

58. Constant temperature Molecular vibrations
When the internal energy of a solid is increased by the application of an external energy source, the molecular vibrations of the substance increases. As these vibrations increase, the substance becomes more and more disordered
Constant temperature
Substances melt at a constant temperature, the melting point. Further increases in temperature (even with continued application of energy) do not occur until the substance is molten

59. 7. Thermal chock
Thermal shock is the name given to cracking as a result of rapid temperature change. Glass and ceramic objects are particularly vulnerable to this form of failure, due to their low toughness, low thermal conductivity, and high thermal expansion coefficients
Thermal shock occurs when a thermal gradient causes different parts of an object to expand by different amounts. This differential expansion can be understood in terms of stress or of strain, equivalently. At some point, this stress overcomes the strength of the material, causing a crack to form. If nothing stops this crack from propagating through the material, it will cause the object's structure to fail

60. Thermal shock can be prevented by:
Reducing the thermal gradient seen by the object, by
changing its temperature more slowly
increasing the material's thermal conductivity
Reducing the material's coefficient of thermal expansion
Increasing its strength
Increasing its toughness, by
crack tip blunting, i.e., plasticity or phase transformation
crack deflection

61. Example.
Borosilicate glass such as Pyrex is made to withstand thermal shock better than most other glass through a combination of reduced expansion coefficient and greater strength, though fused quartz outperforms it in both these respects. Some glass-ceramic materials include a controlled proportion of material with a negative expansion coefficient, so that the overall coefficient can be reduced to almost exactly zero over a reasonably wide range of temperatures

62. 8. wear
Wear is the erosion of material from a solid surface by the action of another solid, or
it is a process in which interaction of surface(s) or bounding face(s) of a solid with the working environment results in the dimensional loss of the solid, with or without loss of material
Wear environment includes loads(types include unidirectional sliding, reciprocating, rolling, impact),speed, temperatures, counter-bodies(solid, liquid, gas), types of contact (single phase or multiphase in which phases involved can be liquid plus solid particles plus gas bubbles)

63. principal wear processes
There are four principal wear processes:
Adhesive wear
Abrasive wear
Corrosive wear
Surface fatigue

64. a. Adhesive wear b. Abrasive wear
Adhesive wear is also known as scoring, galling, or seizing. It occurs when two solid surfaces slide over one another under pressure. Surface projections, or asperities, are plastically deformed and eventually welded together by the high local pressure. As sliding continues, these bonds are broken, producing cavities on the surface, projections on the second surface, and frequently tiny, abrasive particles, all of which contribute to future wear of surfaces
b. Abrasive wear
When material is removed by contact with hard particles, abrasive wear occurs. The particles either may be present at the surface of a second material or may exist as loose particles between two surfaces

65. c. Corrosive wear d. Surface fatigue
Often referred to simply as “corrosion”, corrosive wear is deterioration of useful properties in a material due to reactions with its environment
d. Surface fatigue
Surface fatigue is a process by which the surface of a material is weakened by cyclic loading, which is one type of general material fatigue

66. SUMMARY • Engineering materials don't reach theoretical strength.
• Flaws produce stress concentrations that cause
premature failure.
• Sharp corners produce large stress concentrations
and premature failure.
• Failure type depends on T and stress:
- for noncyclic s and T < 0.4Tm, failure stress decreases with:
- increased maximum flaw size,
- decreased T,
- increased rate of loading.
- for cyclic s:
- cycles to fail decreases as Ds increases.
- for higher T (T > 0.4Tm):
- time to fail decreases as s or T increases.

67. Ideal vs Real Materials
• Stress-strain behavior (Room T):
TS << TS
engineering
materials
perfect 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 more flaws!