introduction fracture mechanics 1
Post on 22-Feb-2018
247 Views
Preview:
TRANSCRIPT
-
7/24/2019 Introduction Fracture Mechanics 1
1/15
Early structural concepts
Some of the structures in earlier have enduredfor ages.
Materials used were brittle type like bricks, stones,
mortar: poor to carry tensile loads.
Avoided fracture possibilities by selecting
appropriate geometric shapes like arches, domes
The structure were designed to carry load by
compression
New structural concepts
Availability of metals lead to change in structural
concepts: allowed tension in structure. (this invited
additional problems like fracture) Designs based on strength allowed a factor of safety
ranging from 2 to 10, but still structures failed by
sudden brittle fracture
Eg. 1919 rupture of Molasses tank in Bostonspilling 2 million gallons of molasses
* When ever there is newmaterial or new design
concepts produces
unexpected results leading
to catastrophic failure
-
7/24/2019 Introduction Fracture Mechanics 1
2/15
-
7/24/2019 Introduction Fracture Mechanics 1
3/15
-
7/24/2019 Introduction Fracture Mechanics 1
4/15
-
7/24/2019 Introduction Fracture Mechanics 1
5/15
Hogging Bending Moment
1943, Liberty ship: a cargo ship
Prior to II world war liberty ships were riveted (very slow process) having no
fracture problems
During war, to accelerate ship building, England sought help from USA. USA
companies offered to build ship faster, by welding joints.
They maintained same geometric shape, ship hull turned out to be a single
envelope of steel.
Ships were sailing across Atlantic and Artic ocean. (cold temperatures). During
which two ships fractured suddenly in to two halves ( brittle fracture). Out of
2700 ships built, 400 ships suffered fractures of various degree.
Analysis
Unequal distribution of cargo and ballast was
causing hogging bending momentWave motion also caused hogging BM,
resulting in tensile stress on the deck.
Welds were produced by semi skilled work
force, which contained crack like flaws
*Negligence during
construction or operation some
times results in catastrophicfailures
-
7/24/2019 Introduction Fracture Mechanics 1
6/15
Flaw
-
7/24/2019 Introduction Fracture Mechanics 1
7/15
Analysis (contd.)
cracks were found to initiate at square hatch
which induced stress concentration due tensile
stress
The high strength steel used for the ship had
poor toughness (Charpy impact test). Heat Affected Zone (HAZ) will have low
ductility, behaving like a hardened material.
Due to rapid cooling, tensile residual stress
are induced. This is equivalent to crack likedefect.
3
Riveted joints
act as crackarrester
welded joints
producecontinuous
crack
-
7/24/2019 Introduction Fracture Mechanics 1
8/15
Conclusion on liberty ship failure
Steel-BCC crystal.
They can fracture by extended slip in some preferred planes producing
plasticity or
Fracture by cleavage under different plane under tensile stress without
plastic deformation, at a stress level below yield strength
Cleavage fracture are predominant at lower temperatures ( at lower
temperature yield strength is higher than fracture strength)
The combined effect of low ductile steel, freezing temperature, presenceof crack like defect (residual tensile stress), crack like defect in the weld lead
to sudden brittle fracture, which initiated at the hatch on the deck due to
tensile service load, crack propagated at fast rate (crack velocity = velocity
of sound) through the entire cross section of the hull breaking ship into twohalves.
Points to be noted At service load tensile stress is induced in the deck due to which crack is
initiates/grows.Presence of microcrack leading to stress concentration
-
7/24/2019 Introduction Fracture Mechanics 1
9/15
Conventional Design Method
Conventional method ensures safety of
structure based on strength characteristics
often structure may have a FS varying
from 2 to 10
Design does not safeguard against possiblefailure by fracture (brittle, ductile, fatigue,
dynamic)
Applied Stress
< YieldStrength
Safe DesignAccept
YieldStrength
Unsafe Design
Redesig
n>
Structure ora structural component
F
f
Design based on Strength of Material Approach
-
7/24/2019 Introduction Fracture Mechanics 1
10/15
Applied Stress
< FractureToughness
Safe DesignAccept
FractureToughness
Unsafe Design
Redesig
n
>
Structure ora structural component
Fracture parameter
Flawsize
F
f
Design based on Fracture Mechanics Approach
Fracture Mechanics Design approach
Fracture mechanics approaches
require that an initial crack size be
known or assumed. For components
with imperfections or defects (such as
welding porosities, inclusions and
casting defects, etc.) an initial crack
size may be known.
Fracture Mechanics ensures safetyagainst fracture failure
Evaluation of fracture parameter
may be required
In presence of visible crack forductile or fatigue loading condition,
FM can predict safety and life of the
structure
-
7/24/2019 Introduction Fracture Mechanics 1
11/15
Ductile Fracture
Intragranular(Transgranular)
Intergranular
Rupture by Necking Rupture by Shear
Ductile fracture is preceded by extensive plasticdeformation
Ductile fracture is caused due to growth and
coalescence of voids (at the sites of inclusion)
Ductile fracture is a slow process , gives enough
precaution before catastrophic failure
Ductile fracture usually follows transgranular path
If the density of inclusion are more along grain
boundary, crack grows along boundaries leading to
fibrous or ductile intergranular fracture If inclusions are not present, voids are formed at
severely deformed regions leading to localized slip
bands and macroscopic instability resulting in
necking or shear fracture
Plasticity retards crack growth and it
provides a factor of safety against over
loading or oversight in design.
-
7/24/2019 Introduction Fracture Mechanics 1
12/15
Voids formed (at particle sites) during plasticdeformation and ductile fracture
-
7/24/2019 Introduction Fracture Mechanics 1
13/15
Voids formed (at non-particle sites) during plastic deformation
and ductile fracture
-
7/24/2019 Introduction Fracture Mechanics 1
14/15
Cleavage
fracture
Intergranular
brittle fracture
Brittle fracture
Fast crack growth without excessive or no
plastic deformation.
Fracture stress will be lower than yield
strength
Brittle fracture may be transgranular(cleavage) or intergranular
Brittle fracture are mostly predominant in
metals with bcc crystal at cryogenic
temperature or at high strain rate.Micro cracks initiated by fatigue loading
may lead to brittle fracture
HAZ induces high tensile residual stress
HAZ also reduces the ductility
Shrinkage tears in weld may also cause
brittle fracture
-
7/24/2019 Introduction Fracture Mechanics 1
15/15
What are the general characteristics of brittle
fracture?Very little general plasticity - broken pieces can be fitted together
with no obvious plastic deformation;
Rapid crack propagation (one third the speed of sound), eg 1 km/s
for steel;Low energy absorption;
Low failure load relative to load for general yield;
Usually fractures are flat and perpendicular to the maximum
principal stress;Fracture always initiates at a flaw or a site of stress concentration.
Examples
Mild steel at low temperature;high strength Fe, Al and Ti alloys;
glass; perspex
ceramics
concretecarrots (particularly fresh ones)
top related