Definitions

Elastic deformation (elasticity)

Deformation is temporary. Returns to its original shape when load is released.

Linear elastic materials

When elastic deformation portion in stress-strain diagram is straight line.

Young’s modulus (aka Elastic modulus)

Can be thought of as stiffness.

Nonlinear elastic materials

When elastic deformation portion in stress-strain diagram is not straight line.

Secant modulus

Equal to the tangent of the line connecting a point in the stress-strain diagram and the origin.

Tangent modulus

Equal to the instantaneous tangent on a point in the stress-strain diagram.

Poisson’s ratio

A tensile stress in a particular direction causes extension (say ) in that direction and contraction in other two directions ( and ). For isotropic materials:

For metals (if not given) can be taken as . Rubber’s poisson’s ratio is which is the maximum possible value, mathematically.

Isotropic materials

Homogenous materials. .

Plastic deformation (plasticity)

When stress is not proportional to strain. Deformation is permanent or non-recoverable or plastic.

Yield stress point

The point where plastic deformation starts in stress-strain diagram.

Yield strength

Stress at yield stress point. Denoted by . Used when the strength of a metal is cited for design purposes.

True yield stress point is very difficult to find practically. Therefore strain offset method is used to find an approximate yield strength.

Strain offset method

A straight line is constructed parallel to the elastic portion of the stress-strain curve at some specified strain offset. The stress corresponding to the intersection of this line and the stress-strain curve is defined as the yield strength .

0.2% proof stress

Yield strength when is used in strain offset method.

For steel

Yield strength is taken as the average stress at the lower yield point. Strain offset method is not required. Upper yield point occurs because of C atoms, and is specific to steel.

Tensile strength

After yielding, the stress necessary to continue plastic deformation increases to a maximum, and then decreases.

Ultimate tensile strength (UTS)

The maximum stress that can be sustained by a material in tension.

Toughness

The strain energy absorbed by a material before fracture.

Fracture

Separation of a solid into more than 1 parts under load or stress.

Based on the type of load:

• Tensile fracture
• Compressive fracture
• Shear fracture
• Fatigue fracture
• Creep fracture

Characterized into 2:

• Ductile fracture
• Brittle fracture

Ductile fracture

Materials show significant amount of plastic deformation prior to fracture. Fracture surface gives cup & cone appearance. Aka. cup-and-cone fracture.

Steps:

1. Specimen forms a neck
2. Cavities start to form within the neck
3. Cavities join with each other and form a crack
4. Crack propagates towards surface perpendicular to stress
5. Direction of crack changes to

Brittle fracture

Little or no plastic deformation prior to fracture. Fracture surface is smooth.

More dangerous than ductile fracture.

• No warning sign
• Crack propagates at very high speeds
• No need for extra stress during crack propagation.

Ductility & Brittleness

Depends on:

• Composition of the material
• Temperature

Ductile to Brittle Transition Temperature

The temperature which a material is:

• brittle below the temperature
• ductile above the temperature

Many steels exhibit this behaviour.