Introduction Fracture Mechanics 1

7/24/2019 Introduction Fracture Mechanics 1

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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


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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


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Flaw


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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


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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


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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


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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


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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.


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Voids formed (at particle sites) during plasticdeformation and ductile fracture


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Voids formed (at non-particle sites) during plastic deformation

and ductile fracture


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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


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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)

Introduction Fracture Mechanics 1

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