## Note on Fundamentals of fractures

• Note
• Things to remember

### Facture of metals

1. Fundamental of fracture
2. Principle of fracture mechanics
3. Crack initiation and propagation

The failure of metal or engineering material is undesirable event for several reasons. There are different types of undesirable condition that appears in materials.

#### What do you mean by fracture? Define fracture in ductile material and in brittle material.

Fracture is defined as separation of body due to different types of stress below the melting point of object. There are two steps in fracture:-

1. Crack formation
2. Crack propagation

Depending upon ability of material to undergo plastic deformation before the fracture two different modes of fracture can be defined:-

1. Ductile fracture
2. Brittle fracture

In ductile materials i.e. most of the metals at temperature not to cold the materials behave as ductile material when there is formation of crack ahead of plastic deformation the crack is stable and it moves in the surrounding region if the amount of stress is increased. Such types of material is more susceptible to ductile fracture.

Ductile fracture is sometimes a desirable effect in the metals. There are different modes of formation of fracture.

1. Necking
2. Formation of microwaves
3. Coalescence of micro voids to form crack
4. Crack propagation by shear deformation
5. Fracture

These type of fracture shown below is known as cup- and –cone fracture, which is called cup – and – cone due tio fact that in the region of fracture there is formation of cup- and – cone.

#### Brittle fracture

Those type of material in which there is no appreciable value of plastic deformation. The propagation of crack is very fast and the material have smaller value of energy absorption during stress-strain cycle are known as brittle material. Such as ceramics, ice, cold metals, the crack is unstable and increases rapidly without increase in applied stress. The fracture or separation appear in this is known as brittle fracture. In brittle fracture crack often propagation by cleavage. The breaking of atomic bonds along specific crystallographic direction is known as cleavage. The two types of brittle fracture are:

1. Transgranular fracture
2. Intergranular fracture

#### Transgranular fracture

In this types of fracture the cracks passes through grains. Macroscopically, the fracture surface may have grainy texture as shown in above

#### Intergranular fracture

In this type of fracture the propagation of crack is along grain boundary. This is due to the grain boundary or by the presence of impurities segregation.

#### Stress concentration

The fracture strength of a brittle said material is related to cohesive force between atoms. The approximate theoretical cohesive strength that of material should be $$\frac{E}{10}$$. ( where E is young’s modulus of elasticity)

This much lower fracture strength is explained by effect of stress concentration ft microscopic flaw. The applied stress is amplified at the tip of microcrack, voids, notches, surface scratches, corner etc that are called stress raiser. The magnitude of this amplification depends on microcrack orientation geometry and dimension.

For long crack orientation perpendicular to the applied stress, the stress is maximum neat crack tip and is given by,

$$\sigma_m=2\sigma_\circ\biggl(\frac{a}{\rho_t}\biggr)^\frac{1}{2}\dotsm(2)$$

Where,

$$\sigma_\circ$$=applied external stress

a=half length of internal flaw or full length of surface flaw

$$\rho_t$$=radius of curvature of crack tip

The ratio of maximum stress near the crack tip and applied stress is known as stress concentration factor. It is denoted by $$K_t$$.

$$\therefore K_t=\frac{\sigma_m}{\sigma_\circ}=2 \biggl(\frac{a}{\rho_t}\biggr)^\frac{1}{2}$$

Crack with sharp tip travel fast than crack having blunt tip.

In ductile material, plastic deformation at a crack tip blunts the crack whereas in a brittle material crack tip is sharp as shown in figure.

figure

#### References:

Callister, W.D and D.G Rethwisch. Material Science and Engineering. 2nd. New Delhi: Wiley India, 2014.

Lindsay, S.M. Introduction of Nanoscience . New York : Oxford University Press, 2010.

Patton, W.J. Materials in industry . New Delhi : Prentice hall of India, 1975.

Poole, C.P. and F.J. Owens. Introduction To Nanotechnology. New Delhi: Wiley India , 2006.

Raghavan, V. Material Science and Engineering. 4th . New Delhi: Pretence-Hall of India, 2003.

Tiley, R.J.D. Understanding solids: The science of Materials. Engalnd : John wiley & Sons , 2004.

1. Different mode of formation of fracture

1. Necking
2. Formation of microwaves
3. Coalescence of micro voids to form crack
4. Crack propagation by shear deformation
5. Fracture

2.

$$\sigma_m=2\sigma_\circ\biggl(\frac{a}{\rho_t}\biggr)^\frac{1}{2}$$

$$\therefore K_t=\frac{\sigma_m}{\sigma_\circ}=2 \biggl(\frac{a}{\rho_t}\biggr)^\frac{1}{2}$$

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