Failure mechanism part: Fracture

i. Fracture
ii. Fatigue failure
iii. creep
Keval K. Patil, M.E.-DESIGN, (kevalpatil@gmail.com)
1

Part 1
2

 DEFINATION: Simple 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)
 A fracture is the separation of an object or material into two or more pieces under the action of stress.
 The fracture of a solid usually occurs due to the development of certain displacement discontinuity
surfaces within the solid.
 If a displacement develops perpendicular to the surface of displacement, it is called a normal tensile
crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is
called a shear crack, slip band, or dislocation.
 Fracture strength or breaking strength is the stress when a specimen fails or fractures.
 Types of Fracture
 Ductile fracture
 Brittle fracture
Keval K. Patil, M.E.-DESIGN, (kevalpatil@gmail.com) 3

 Fracture mechanics is the field of mechanics concerned with the study of the
propagation of cracks in materials.
 In modern materials science, fracture mechanics is an important tool in improving
the mechanical performance of engineering components.
 It applies the physics of stress & strain, in particular the theories of elasticity &
plasticity, to the microscopic crystallographic defects found in real materials in
order to predict the macroscopic mechanical failure of bodies.

 When a ductile material has a
gradually increasing tensile stress,
it behaves elastically up to a
limiting stress & then plastic
deformation occurs.
 As stress is increased, the cross
sectional area of the material is
reduced & a necked region is
produced.
 With a ductile material, there is a
considerable amount of plastic
deformation before failure occurs in
the necked region

1. Necking
2. Small Cavities Formation
3. Formation of Crack
4. Propagation of crack
5. Cup & Cone Fracture

 Necking, in engineering or materials
science, is a mode of tensile deformation
where relatively large amounts of strain
localize disproportionately in a small
region of the material.
 With elastic strain the material becomes
plastically deformed & neck formation
process starts
Necking
Force
Applied (F)

 Within the neck, small cavities or voids are
formed.
 These develop as a result of the stress causing
small particle of impurities or other
discontinuities in the material to either fracture or
separate from metal matrix.
 More such nuclei are available to trigger the
development of these cavities, the less the
material will extend before fracture & less ductile
the material
 As purity of material increases, ductility of the
material also increases.
Small
cavities
forming.
Force
Applied (F)

 Small cavities, or micro voids, form in the
interior of the cross section
 Those cracks enlarge, come together, &
coalesce to form an elliptical crack, which has
its long axis perpendicular to the stress
direction.
 The crack continues to grow in a direction
parallel to its major axis by this micro void
coalescence process.
Force
Applied (F)
Formation of crack
perpendicular to
force applied
Force
Applied (F)
Propagation of
crack
perpendicular to
force applied
10

 Finally, fracture ensues by the rapid propagation of
a crack around the outer perimeter of the neck by
shear deformation at an angle of about 45 degree
with the tensile axis this is the angle at which the
shear stress is a maximum.
 Sometimes a fracture having this characteristic
surface contour is termed a cup-and-cone fracture
because one of the mating surfaces is in the form
of a cup, the other like a cone.
 In this type of fractured specimen the central
interior region of the surface has an irregular &
fibrous appearance, which is indicative of plastic
deformation.
Cup Cone
cup-and-cone fracture

 Brittle fracture takes place without any appreciable deformation & by rapid crack
propagation.
 The direction of crack motion is very nearly perpendicular to the direction of the applied
tensile stress & yields a relatively flat fracture surface
 When gradual tensile load is applied on material in tensile test, at the end of elastic limit,
without any prior indication material breaks.
 This type of fracture is called as Brittle Fracture

 Factors affecting the fracture of a material includes,
A. Stress Concentration (Notch Sensitivity)
B. The speed with which the load is applied.
C. The temperature.
D. Thermal shock loading.

 Notch sensitivity is defined as, ‘A reduction in properties due to the
presence of stress concentration’.
 Any kind of irregularities produces stress concentration in material,
such as
 Crack.
 A grain boundary.
 An internal corner of engineering plant.
 If you want to break a small piece of material, one way is to make a
small notch in the surface of the material & then apply a force.

 The presence of a notch or any
sudden change in section of a
piece of material, can very
significantly change the stress at
which occurs
 The notch or sudden change in
section produced in the metal, is
called as stress concentration.
 They disturb the normal stress
distribution & produce local
concentration of stress.

 A sudden application of load or impact loading
may lead to fracture where the same stress is
applied more slowly, it would not break.
 The Charpy & Izod tests give a measure of a
behaviour of notched sample of material where
subject to a sudden impact load.
 The results are expressed in terms of the energy
needed to break a standard size test piece.
 The smaller the energy needed, the easier it is
for failure.
 Brittle materials needs lower energies for
failure whereas Ductile materials needs higher
energies for failure

 The temperature of material can effect its behaviour when subject to stress.
 Many materials which are ductile at a higher temperature are brittle at lower
temperature.

 Pouring hot water in cold glass, can cause the glass to
crack.
 This is the cause of thermal shock loading.
 The layer of glass in contact with the hot water trying
to expand but is restrained by the colder outer layer of
the glass.
 These layers are not heating up quickly because of poor
thermal conductivity of glass.
 Result is the setting up of stress which can be
sufficiently high to cause of brittle glass

 One of the primary functions of Charpy & Izod tests is to determine whether or
not a material experiences a ductile-to-brittle transition with decreasing
temperature &, if so, the range of temperatures over which it occurs.
 The ductile-to-brittle transition is related to the temperature dependence of the
measured impact energy absorption.
 This transition is represented for a steel by curve
 At higher temperatures the impact energy is relatively large, in correlation with
a ductile mode of fracture.
 As the temperature is lowered, the impact energy drops suddenly over a
relatively narrow temperature range, below which the energy has a constant but
small value; that is, the mode of fracture is brittle.

 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
21

22
• Pre-WWII: The Titanic 10th April 1912 • WWII: Liberty ships
• Problem: Used a type of steel with a DBTT ~ Room temp.

 Common BCC (body centered cubic type of atomic structure) metals
become brittle at low temperature or at extremely high rates of strain.
 Many FCC ( face centered cubic ) metals, on the other hand, remain
ductile even at very low temperatures.
 Polycrystalline HCP ( hexagonal closed packing ) metals are brittle, as
there are not enough slip systems to maintain grain boundary integrity.

 Following factors affect Ductile – Brittle transition temperature.
 Transition temperature increases
 When grain size of material increases.
 When alloying elements are added in the material.
 When impurities in metal increases.
 When percentage of carbon in steel increases.

 Defects & cracks are present in all engineering materials.
 They may be introduced during solidification or heat treatment stages of
the material.
 The fracture resisting capacity of machine component or engineering
structures must be evaluated in the presence of cracks.
 The fracture resistance of a material in the presence of a crack or
discontinuities is known as its fracture toughness.
 From Griffith type of approach, the fracture toughness is defined by the
critical value of parameter ‘Gc’. ‘Gc’ gives the value of the strain energy
release per unit area of the crack surface, when unstable crack extension
(lead to fracture) take place. For an elastic crack of length ‘2c’,

 Fracture mechanics was developed during World War I by English aeronautical engineer, A. A.
Griffith, to explain the failure of brittle materials.
 According to Griffith, there are micro cracks in the metal that causes local concentration of
stress to values high enough to propagate the crack & eventually to fracture of metal.
 In Griffith theory, an energy method is employed to estimate the stress necessary to cause a
crack to propagate
 The Griffiths equation describes the relationship between applied normal stress and crack
length at brittle fracture.
 Griffith’s work was motivated by two contradictory facts:
 The stress needed to fracture bulk glass is around 100 Mpa. (An amorphous metal also
known metallic glass or glassy metal)
 The theoretical stress needed for breaking atomic bond is approximately 10,000 Mpa.

 Consider lens ( elliptical ) shaped crack of length ‘2c’.
 Material of 1 unit thickness.
 Crack run from the front to back face.
 Longitudinal tensile stress (σ) sigma is applied
 The crack tends to increase its length in transverse direction.
 If crack spreads, the surface area of crack increases, while the elastic strain
energy stored in the material decreases, because strains cannot be
continuous across the cracked region.
 (σ) is surface energy per unit area of the material.
 No energy (elastic) is stored in cylindrical volume around crack.
 Elastic energy is released when crack is introduced.

 Griffith was of the opinion that, “ A crack will propagate ( travel)
when decrease in elastic strain energy is at least equal to the energy
required to create a new crack.
 The surface energy associated with a flat crack of length 2c & unit
thickness is 4Cγ ,, ( where γ = surface energy/unit area of crack
surface)
 Taking into consideration this plastic deformation of the surface of
the crack requiring energy ‘p’ per unit area, the total energy required
to create crack is,
 Uσ = 4C(γ +p)
 This energy is supplied by the elastic strain energy released by
formation of crack

 Total energy per unit volume (Ue) when crack
introduced is,
Ue = [(Π/4)*(2C)^2 *(t)]* [1/2*σ* e^2]
 t= unit thickness = 1;
 2C = length of crack;
 E= Young’s Modulus;
 σ= stress applied;
 e= strain in material.
 We know that, e= σ/E.

 Griffith's theory provides excellent agreement with experimental data for
brittle materials such as glass.
 For ductile materials such as steel, though the relation still holds, the
surface energy (γ) predicted by Griffith's theory is usually unrealistically
high.
 A group working under G. R. Irwin at the U.S. Naval Research Laboratory
(NRL) during WW II realized that plasticity must play a significant role in
the fracture of ductile materials.
 In ductile materials (& even in materials that appear to be brittle), a plastic
zone develops at the tip of the crack.
 As the applied load increases, the plastic zone increases in size until the
crack grows & the material behind the crack tip unloads.

 The plastic loading & unloading cycle near the crack tip leads to the
dissipation of energy as heat.
 Hence, a dissipative term has to be added to the energy balance
relation devised by Griffith for brittle materials.
 In physical terms, additional energy is needed for crack growth in
ductile materials when compared to brittle materials.
 Orwin's strategy was to partition the energy into two parts:
 The stored elastic strain energy which is released as a crack grows. This is the
thermodynamic driving force for fracture.
 The dissipated energy which includes plastic dissipation & the surface energy
(& any other dissipative forces that may be at work).

 The dissipated energy provides the thermodynamic resistance to
fracture.
 Then the total energy dissipated is
 where γ is the surface energy & Gp is the plastic dissipation (&
dissipation from other sources) per unit area of crack growth.
 The modified version of Griffith's energy criterion can then be written
as

C=

Failure mechanism part: Fracture

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