Chapter 8 mechanical failure

Mechanical Failure
ISSUES TO ADDRESS...

Chapter reading 8

• How do cracks that lead to failure form?
• How is fracture resistance quantified? How do the fracture
resistances of the different material classes compare?
• How do we estimate the stress to fracture?
• How do loading rate, loading history, and temperature
affect the failure behavior of materials?

Ship-cyclic loading
from waves.

Computer chip-cyclic
thermal loading.

MSE-211-Engineering Materials

Hip implant-cyclic
loading from walking.

1 1

Mechanical Failure
Why study failure?

Design of a component or structure: Minimize failure possibility

It can be accomplished by understanding the mechanics of failure
modes and applying appropriate design principles.
Failure cost
1. Human life

2. Economic loss

3.Unavailability of service

Failure causes:
1. Improper material selection

2. Inadequate design 3. Processing

Regular inspection, repair and replacement critical to safe design

2

Fracture

Fracture is the separation of a body into two or more
pieces in response to an imposed stress

Steps in Fracture:
 Crack formation
 Crack propagation


3

Fracture Modes
Depending on the ability of material to undergo plastic deformation
before the fracture two fracture modes can be defined - ductile or
brittle.

Ductile fracture - most metals (not too cold):
 Extensive plastic deformation ahead of crack
 Crack is “stable”: resists further extension
unless applied stress is increased

Brittle fracture - ceramics, ice, cold metals:
 Relatively little plastic deformation
 Crack is “unstable”: propagates rapidly without
increase in applied stress
Ductile fracture is preferred in most applications

4

Ductile Vs Brittle Fracture
Fracture
behavior:

Very
Ductile

Moderately
Ductile

Brittle

%AR or %EL

Large

Moderate

Small


5

Ductile Fracture
• Evolution to failure:

(a)

(b)

(c)

(a) Necking
(b) Formation of microvoids
(c) Coalescence of microvoids to form a crack
(d) Crack propagation by shear deformation
(e) Fracture


(d)

(e)
Cup and cone
fracture

6

Ductile Vs Brittle Fracture
ductile fracture

brittle fracture

(Cup-and-cone fracture in Al)

Brittle fracture in a mild steel


7

Ductile Fracture

(a) SEM image showing spherical dimples resulting from a
uniaxial tensile load representing microvoids. (b) SEM image of
parabolic dimples from shear loading.

8

Brittle Fracture
Arrows indicate point at failure origination

Distinctive pattern on the fracture surface: V-shaped “chevron”
markings point to the failure origin.

9

Brittle Fracture
Lines or ridges that radiate from the origin of
the crack in a fanlike pattern


10

Transgranular fracture
Fracture cracks pass through grains.


11

Intergranular fracture: Fracture crack propagation is
along grain boundaries (grain boundaries are weakened
or embrittled by impurities segregation etc.)


12

Example: Pipe Failures
• Ductile failure:
-- one piece
-- large deformation

• Brittle failure:
-- many pieces
-- small deformations


13 13 13

Fracture Mechanics

Studies the relationships between:
material properties
stress level
crack producing flaws
crack propagation mechanisms


14

Stress Concentration
Measured fracture strength is much lower than predicted by calculations
based on atomic bond energies. This discrepancy is explained by the
presence of flaws or cracks in the materials.

The flaws act as stress concentrators or stress raisers,
amplifying the stress at a given point.
The magnitude of amplification depends on crack
geometry and orientation.


15



16

If the crack is similar to an elliptical
hole through plate, and is oriented
perpendicular to applied stress, the
maximum stress, at crack tip
1/ 2

a
s m  2s o  
 
where
 t

t = radius of curvature
so = applied stress
sm = stress at crack tip
a = length of surface crack or ½
length of internal crack


17

1/ 2

a
s m  2s o  
 
 t

(1)

The stress concentration factor is
A measure of the degree to which an external
stress is amplified at the tip of a crack.

a 
sm  2so    Ktso
t 
1/ 2

Rearranging equation 1


18

Engineering Fracture Design
• Avoid sharp corners!
s
smax
Stress Conc. Factor, K t =
s0
sw
max

r,
fillet
radius

2.5

h

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.)

2.0

increasing w/h

1.5

1.0

0

0.5
1.0
sharper fillet radius

r/h

19 19

Crack propagation
Cracks with sharp tips propagate easier than cracks having blunt tips
1/ 2

a
s m  2s o  
 
 t

In ductile materials, plastic deformation at a crack tip “blunts” the crack.


20

Crack propagation
Critical stress for crack propagation

γs = specific surface energy
When the tensile stress at the tip of crack exceeds the critical stress value
the crack propagates and results in fracture.


21

EXAMPLE PROBLEM 8.1 Page 244
A relatively large plate of a glass is subjected to a tensile stress of 40
MPa. If the specific surface energy and modulus of elasticity for this
glass are 0.3 J/m2 and 69 GPa, respectively, determine the maximum
length of a surface flaw that is possible without fracture.

𝐸 = 69 𝐺𝑃𝑎

𝛾 𝑠 =0.3 J/m2

𝜎 = 40 𝑀𝑃𝑎
Rearranging the equation

2𝐸𝛾 𝑠
𝑎=
𝜋𝜎 2

𝑎 = 8.2 * 10-6 m


22

Home Work Problems
Exercise Problems 8.1-8.4


23

Fracture Toughness
• Fracture toughness measures a material’s resistance to
fracture when a crack is present.
• It is an indication of the amount of stress required to
propagate a preexisting flaw.

𝐾 𝑐 = 𝜎 𝑐 𝜋𝑎
𝐾 𝑐 = Fracture toughness


24

Fracture Toughness
𝑲 𝒄 is a material property depends on temperature, strain rate
and microstructure.
 The magnitude of Kc diminishes with increasing strain rate
and decreasing temperature.
 Improvement in yield strength wrought by alloying and
strain hardening generally produces corresponding decrease
in Kc .
 Kc normally increases with reduction in grain size as
composition and other microstructural variables are
maintained constant.


25

Impact Fracture Testing
Testing fracture characteristics under high strain rates

Two standard tests, the Charpy and Izod, measure the impact
energy (the energy required to fracture a test piece under an
impact load), also called the notch toughness


26

Impact Fracture Testing
(Charpy)

Izod

final height

initial height

27

Ductile-to- brittle transition
As temperature decreases a ductile material can become
brittle - ductile-to-brittle transition.
The ductile-to-brittle transition can be measured by impact testing:
the impact energy needed for fracture drops suddenly over a
relatively narrow temperature range – temperature of the ductile-tobrittle transition.

The ductile to-brittle transition is related to the temperature
dependence of the measured impact energy absorption


28

• Ductile-to-Brittle Transition Temperature (DBTT)...

Impact Energy

Low strength (FCC and HCP) metals (e.g., Cu, Ni)

Low strength steels(BCC)
polymers
Brittle

More Ductile

High strength materials

Temperature

Adapted from Fig. 8.15,
Callister & Rethwisch 8e.

Ductile-to-brittle
transition temperature

29 29

Design Strategy:
Stay Above The DBTT!
• Pre-WWII: The Titanic

• WWII: Liberty ships

• Problem: Steels were used having DBTT’s just below
room temperature.

30

Fatigue
Fatigue
Failure under fluctuating / cyclic stresses
e.g., bridges, aircraft, machine components, automobiles,etc..

• Stress varies with time.

smax
sm
smin


s
S
time

31

Fatigue
Fatigue failure can occur at loads considerably lower
than tensile or yield strengths of material under a static
load.
Estimated to causes 90% of all failures of metallic structures
Fatigue failure is brittle-like (relatively little plastic
deformation) - even in normally ductile materials. Thus
sudden and catastrophic!
Fatigue failure proceeds in three distinct stages: crack
initiation in the areas of stress concentration (near stress
raisers), incremental crack propagation, final catastrophic
failure.

32

Fatigue
CYCLIC STRESSES

Periodic and symmetrical
about zero stress

1.Reversed stress cycle

2.Rpeated stress cycle
Periodic and asymmetrical
about zero stress


33

Fatigue
CYCLIC STRESSES

3.Random stress cycle

Random stress fluctuations


34

Fatigue
CYCLIC STRESSES

Mean stress (𝜎 𝑚 )


35


36

Fatigue
S — N curves
(stress — number of cycles to failure)

Fatigue properties of a material (S-N curves) are tested in
rotating-bending tests in fatigue testing apparatus

Result is commonly plotted as S (stress) vs. N (number of
cycles to failure)

37

S — N curves
Fatigue limit (endurance limit) occurs for some materials
(e.g. some Fe and Ti alloys). In this case, the S—N curve
becomes horizontal at large N, limiting stress level. The fatigue
limit is a maximum stress amplitude below which the material
never fails, no matter how large the number of cycles is.
For many steels,
fatigue limits
range between
35% and 60%
of the tensile
strength.


38

S — N curves
In most non ferrous alloys(e.g., Aluminum, Copper,
Magnesium) S decreases continuously with N. In this
cases the fatigue properties are described by
Fatigue strength: stress at which

fracture occurs after a
specified number of cycles (e.g.
107)
Fatigue life: Number of cycles to
fail at a specified stress
level


39


40

Fatigue
Fracture surface characteristics
Beach marks and striations


41

Creep
Creep is a time-dependent and permanent deformation
of materials when subjected to a constant load or stress.
For metals it becomes important at a high temperature
(> 0.4 Tm). Examples: turbine blades, steam
generators, high pressure steam lines.
Polymers are specially sensitive to creep.

For details read the book pages 265-267


42

Stages of Creep


43

Stages of Creep
1. Instantaneous deformation, mainly elastic.
2. Primary/transient creep. Slope of strain vs. time
decreases with time: strain-hardening
3. Secondary/steady-state creep. Rate of straining is
Constant
4. Tertiary. Rapidly accelerating strain rate up to
failure:
formation of internal cracks, voids, grain boundary
separation, necking, etc.

44

Parameters of creep behavior
The stage of secondary/steady-state creep is of longest
.

∆𝜺
.is the
∆𝒕

duration and the steady-state creep rate 𝜺 𝒔 =
most important parameter of the creep behavior in long-life
applications e.g. nuclear power plant component.
Another parameter, especially important in short-life
creep situations, is time to rupture, or the rupture
lifetime, tr.. e.g., turbine blades in military aircraft and
rocket motor nozzles, etc….


45

Creep: stress and temperature effects


46

Chapter 8 mechanical failure

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