Fracture Specimen

• To Visualize whether a crack of given length in a material of known fracture toughness is dangerous, because it will propagate to given stress levels.

• To visualize the driving force on a crack to characterize the material's resistance to fracture.

Fracture Specimen

• Crack

• Fatigue

Fracture

• Fracture– A fracture is the (local) separation of an object or material into two, or

more, pieces under the action of stress.• The process of Fracture can be considered to be made up of two

components– Crack Initialization. – Crack propogation• Fractures are of two types

Brittle fracture Ductile fracture

Fracture Specimen

• The first Explanation of discrepancy between the observed fracture strength of the crystals and the theoritical cohesive strength was proposed by griffith.

• Griffith proposed that “ A crack will propogate when the decrease in elastic strain energy is at least equal to the energy required to create the new crack surface.

• Let us consider a elliptical crack of length 2c subjected to axial tensile load, where tensile stress is given by σ.

Griffith & Irwin theory of brittle fracture

Fracture Specimen

• Total energy of the system = u• U= ue + us

• Where • ue = elastic Strain Energy• us = Energy in creating new

crack surface area.

• When crack extends by δc, the • ue = Decreases• us = Increases• For equilibrium dU/dC is= 0;•

Fracture Specimen

• Let us consider a edge crack whose length is a and subjected to tensile loading.

• As the crack grows longer (a increases), the quadratic dependence of strain energy on a eventually dominates the surface energy,

• Beyond a critical crack length ac the system can lower its energy by letting the crack grow still longer.

• Up to the point where a = ac, the crack will grow only if the stress is increased.

• Beyond that point, crack growth is spontaneous and catastrophic.

Fracture Specimen

• The value of the critical crack length can be found by setting the derivative of the total energy S + U to zero:

Critical stress

Fracture Specimen

As per graffiti : Critical stress expression

• For ductile materials the relation ship for Critical stress is given by

• Where is critical strain energy release rate

Fracture Specimen

The variation of elastic strain energy and surface energy for formation of new crack area is presented in the following animation.The parameters of observation are

Crack propogationVariation of Elastic strain energyVariation of Surface energyCritical crack length.

The variation of elastic strain energy and surface energy for formation of new crack area is presented in the following animation.The parameters of observation are

Crack propogationVariation of Elastic strain energyVariation of Surface energyCritical crack length.

Fracture Specimen

START

Fracture Analysis

Fracture Specimen

Fracture Analysis

Fracture Specimen

Fracture Analysis

Fracture Specimen

Fracture Analysis

Fracture Specimen

Fracture Analysis

Fracture Specimen

Check your understanding

• The _________ is a measure of material toughness.

• Resistance to crack propagation

• Critical stress intensity factor

• Geometry of object

• All the above

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Fracture Specimen

Important information about crack and its nature is obtained from  

o Stress strain Curve

o Material properties

o Physical observation of the object under test

o  Gross Microscopic Examination of the fracture surface.   .

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Fracture Specimen

• If 'a' is crack length and ' ac ' is critical crack length, up to which point the crack will grow only if the stress is  increased.• up to any length

• Up to ac

• Up to the geometric length of the object

• Up to half of length.

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Fracture Specimen

• The cohesive strength of silica fiber if E= 95 Gpa and a0=.16 nm , surface energy per unit area=1 J/sq,m is -----------?

•   20 Gpa

• 24.4 Gpa

• 35.6 Gpa

• 12.2 Gpa

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Fracture Specimen

The crack propogation in brittle materials compared to ductile materials is

o Slow

o fast

o Crack propogation is sameo o No comparision

Fracture Specimen

Resources

Books:

Mechanical metalurgy by George E dieter.

Reference Links:

http://www.efunda.com/formulae/solid_mechanics/fracture_mechanics/fm_intro.cfm

http://www.dsto.defence.gov.au/publications/1880/DSTO-GD-0103.pdf

http://ecommons.library.cornell.edu/handle/1813/3075

http://pcwww.liv.ac.uk/rockdef/lectures/3%20Griffith%20theory.pdf