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Materials for Damage Tolerant Design

When a material may fail at a stress much

below its strength?Why ceramics are not as popular as metals for

structural design despite ceramics offer the best

specific strength and specific modulus?

Failure

Ductile BrittleIn the presence of a

crack, brittle failure can

initiate much below the

yield strength of the

material leading to fastfracture

Ductile failure initiates

at yield strength and the

material can fracture

after an appreciable

amount of plastic flow

Almost every engineering design is required to be damage tolerant, however, some applications may require

stringent materials selection to prevent failure. e.g. pressure vessels, aircraft, railroad components etc.

Hatfield, England rail accident, Oct 17, 2000)

A material may be prone to failure if a crack or void is present on the surface

or inside the bulk and this depends on some specific properties of the material

Crackgeometryin a tensileelement. Theploton therightshows thestress distributionaround thecrack

tipfor a particularcase ofgeometryand loading.

An edge crack under tensile loadingy =

1 + 2c

d

d

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r

x

z

x =

KI

(2r)1/2

cos

2

1 - sin

2

sin3

2

+

y =

KI

(2r)1/2cos

21 + sin

2sin

3

2+

xy =

KI

(2r)1/2cos

2sin

2cos

3

2+

Stress field ahead of a crack tip for linearly elastic and isotropic materials

(Ref: Page 324-326, N. E. Dowling , 3rd Edition)

y

z = 0 (plane stress)

yz

= zx

= 0

KI = lim (yr, 0

This equation is expressed in more convenient form (using

the dimensional analysis) as,

KI = Y

[Where c is the half of the crack length in the bulk of the

material, is the nominal stress and Y is a constant

known as shape factor and it depends on the ratio c/b,

increasing as the ratio increases]

2c

b

Toughness vs. Fracture toughness

Which material would you

choose for making pole vault?

Aluminium

Steel

GFRP/CFRP

Bamboo

Olympic record for pole vault

GFRP

CFRP

Bamboo, 1896

5.96 m

2008

5.97 m

2012

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Toughness is the ability of a material to store energy

before it fails completely,

Stress

Strain

or, it is the amount of energy releasedwhen the material is allowed to fully

relax.

Toughness is different from

resilience as the later is the

amount of energy stored for themaximum elastic deformation

Total work done in peeling the tape = Strain energy release perunit area (Gc) x New surface area created

M.g.a = Gc.t.a

Gc = M.g/t

Measuring toughness

Toughness is the amount of energy stored in a material up to the point of failure whereas fracture

toughness is defined as the measure of materials resistance to crack propagation

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Figure 4.2: An edge crack under tensile l oading

Energy approach to fracture toughness calculation

W Uel + Gc t c-Uel = Gc t c

Gc = 2 c / 2E

KI = ( c)1/2 = (E Gc)1/2

KI = Y ( c)

Gc = surface energy

Uel = - 2

2E

c2t

2

-Uel

c= Gc t

Stress intensity

factorY is a shape factor. We can take it as unity if the

value of Y is not given in a design problem.

Fast fracture at fixed displacement: when a plate is clamped in tension so that the upper and

lower ends are fixed

This equation is valid

only for a crack at the

edge/surface

Change in elastic

energy

Energy absorbed in

making unit area of

the crack

Fracture toughness is the critical stress intensity factor, K IC

This 2 can be neglected

as the volume calculation

for total strain was an

underestimation.

GFRP 10-100 20-60

If glass fibre and most of the polymers have low Gc and Kc then why GFRPs have higher Gc and

Kc compared to both glass fibre and plastics?

The fracture toughness of polystyrene and Low Density Polyethylene (LDPE) are about the same (1 MN

m-3/2) but LDPE has very high resistance to crack growth while polystyrene is brittle. Explain why?

Ductile

Brittle

Verybrittle

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Mode I Mode IIMode III

Modes of fracture

Mongolian tough horses

Mechanisms of material failure/fracture

Ductile tearing by plastic deformation is the primary mechanism of failurefor ductile metals and polymers above the DBTT or glass transition

temperature

Ref: fig 8.35 from Mechanical

Behavior of Materials by Dowling

Ref: fig 4.6 from Mechanical Behavior of

Materials by DowlingRef: fig 4.5 from Mechanical Behavior of

Materials by Dowling

Necking

Ductile drawing

Appearance of a ductile failure surface (Co-Fe-V alloy)

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Ductile polymers

Ductile metals

Ref: fig 4.9& 4.10 from Mechanical Behavior of Materials by Dowling

What are the factors that

ductile behaviour depend

upon?

Temperature

Strain rate

Brittle fracture mechanism:

For a ductile material there

will be appreciable plastic

deformation at the crack tip

which will stop further

growth of the crack

For brittle material there is no

or very little plastic

deformation at the crack tip

and the failure takes place by

the cleavage of the atomic

planes.

Fig 14.3 from textbook

Fracture often starts at sharp corners of a material or at places where

there is residual stress concentration such as welded joints

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Appearance of a brittle

failure surface (Co-Fe-

V alloy)

Smooth cleaved surface

Atomistic aspect of brittle fracture:

http://www.mrs.org/membership/preview/may2000bull/Gumbsch.pdf

Ref: fig 8.35 from Mechanical

Behavior of Materials by Dowling

Intergranular brittle fracture (Source: Liam)

Transgranular brittle fracture: In this type of crack

propagation the crack travels across different

grains of the material. The crack may change

direction as it enters a different grain because the

crack propagates through a plane of least

resistance.

Intergranular brittle fracture: In this type of

fracture cracks move along grain boundaries and

not through any grain. For such materials grainboundaries tend to be weaker and hence requires

least energy.

Grains Grain boundaries

Atomicplanes

Hydrogen embrittlement renders steel weaker as

hydrogen reacts with the iron carbide present at the

grain boundaries to form methane gas

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Intergranular brittle fracture (Source: Liam) Embrittled cast steel pneumatic wrench (Ref.

Practical failure analysis, Vol. 2(5), 2002 , page 37)

Transgranular cleavage fracture (Ref. Practical failure

analysis, Vol. 2(5), 2002 , page 37)

Failure mechanism for composites and natural fibers

Fig 14.4 and 14.5 from Ashby and Jones

For composites, fibres act as

crack stopper. When a crack

meets a fibre it starts running

parallel to the fibre leading to

some de-bonding between the

fibre and the matrix.

For rubber toughened

polymers, the stress at the

crack tip is used to deform

rubber particles and thus

further propagation of the

crack is minimized.

Woods are stronger along the fibre length direction. For

example it is easier to peel the fibres of a bamboo but it is

very strong when pulled along its fibre length.