Stress Strain Plot

The below properties can be observed in a stress-strain plot.

• Elastic region
• Yield point
• Proof stress
• Plastic portion - steadily decreasing slope
• Ultimate tensile strength
• Localization of the deformation
• Young’s modulus
• Upper and lower yield stresses
• Fractural strength

Yield stress point

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

Yield strength

Stress at yield stress point. Denoted by $\sigma_y$. 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 $\sigma_y$. $$

0.2% proof stress

Yield strength when $0.002$ 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 $\ce{C}$ atoms, and is specific to steel. $$

Observables

Note

After yield point, gradient of the stress-strain curve decreases up to the necking point. This is an indication that the material is becoming stronger and harder.

Ductility

Higher strain at fracture or failure strain.

Implies:

• Greatest percentage elongation

Stiffness

Slope of the elastic region. Steeper line means more stiffness.

Strengthness

• For ductile materials: yield stress
• For brittle materials: fracture stress

Flexibility

Higher strain in elastic region.

Toughness

Area under the curve, until the breaking point. Higher area means the higher toughness.

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.

$$\text{UTS} = \frac{\text{max load}}{\text{original cross-sectional area}}$$

Necking starts after UTS point.