Tensile Stress-Strain Behaviour

Why is a tensile test performed?

To understand how a material behaves under load, including:

• Stress–strain relationship (elastic region)

• Behaviour beyond elastic limit

• Strength in tension

• Amount of extension before failure

What does a tensile test measure directly?

• Force (P) using a load cell

• Extension (x) using an extensometer

Why don’t we use load–extension data directly?

Because they depend on specimen size → not material properties
→ We convert to stress and strain (size-independent)

Define engineering stress.

Force divided by original cross-sectional area

Define engineering strain.

Extension divided by original length

What is Young’s modulus?

Stiffness of a material

Where is Young’s modulus found on the graph?

Gradient of the initial linear region

What does a high Young’s modulus mean?

Material is stiff (resists deformation)

What is yield strength?

Stress at which plastic deformation begins

What is proof stress?

Stress at a specified strain offset (e.g. 0.2%)
→ Used when yield point is unclear

What is ultimate tensile strength (UTS)?

Maximum stress reached on the curve

Why is proof stress useful?

Some materials don’t have a clear yield point

What is Poisson’s ratio?

Ratio of lateral contraction to axial extension

Why is there a negative sign?

Lateral strain is opposite in direction to axial strain

Typical values of Poisson’s ratio?

• Ceramics: ~0.2

• Metals: ~0.3–0.35

• Polymers: ~0.35–0.4

What does ν = 0.5 imply?

Constant volume deformation

What is elastic deformation?

Reversible deformation (material returns to original shape)

What is plastic deformation?

Permanent deformation after load removal

What happens after yield point?

Plastic deformation begins

What is work hardening?

Increase in strength as material is plastically deformed

What happens during unloading after plastic deformation?

• Linear unloading

• Same slope (E unchanged)

• Higher yield stress on reloading

What is ductility?

Ability to plastically deform before fracture

What is a limitation of % elongation?

Depends on gauge length → not geometry-independent

Why use an extensometer instead of crosshead displacement during a tensile test?

Avoids errors due to:

• Machine deformation

• Fixture movement

Why test multiple specimens?

Improve reliability (reduce experimental variation)

Is stiffness a material property?

No → depends on geometry → F/e

Is stress a material property?

No it is a measure of loading on a specimen, not on how the material behaves

Is Young’s modulus a material property?

Yes → intrinsic

Why does stress drop after UTS?

Necking reduces cross-sectional area, so the load that the specimen can carry decreases. Hence engineering stress will also decrease (but true stress increases)