tensile test 2

the rest of the tensile test 1

Determination of 0.2% proof stress : -

Some metallic substance doesn't show any yield point a tension test e.g. hard steel, non-ferrous metals and alloys. In this case the 0.2% proof stress found instead of the yield point. The 0.2% proof stress is defined as stress by which plastic deformation of 0.2% take place.
and determined by two methods : -

1-By loading and unloading the tension specimen for several times and increasing the
load gradually in each time. The elongation is measured after every unloading until we
have a plastic elongation equals to 0.2%, then the stress corresponding to that strain is
the 0.2 proof stresses.
2-From stress-strain diagram or a part of it:-
From the point representing 0.2% elongation on the ?-axis a straight line is drawn parallel to that representing "Hook's law". The projection of the point intersection "N" of the line with the curve on the ?-axis gives the 0.2 proof stress, as shown in the following figure.

Example of stress-strain curve and the method of calculation of the 0.2 proof stress.

The engineering and real (true) stress–strain diagram

The engineering stress (S) is determined by dividing the applied force (F) by the initial area (Ao) of the specimen:

S=F/Ao

The strain (e) is determined by dividing increase in the length of the specimen (dL in mm) by the original length(Lo) :

e = ΔL / L_o

The real (true) stress (σ) and strain (ε) values are related to the instantaneous cross
sectional area (A) of the specimen and the specimen’s length (L).

True stress: σ = F / A ............................................(1)

True strain: ε = dL / L ............................................(2)

From the volume constancy; AL = Ao Lo ............................(3)

Substituting eq. (3) into eq. (1)

σ = ( F / Ao ) . ( L / Lo )

= S ( ( Δ L+ Lo ) / Lo )

True stress, σ = S (e + 1 )

The true strain is equal to the integration of the incremental stain:
L
ε = ∫ dL/L
Lo

= Ln ( L /Lo)

= Ln ( ( Δ L+ Lo ) / Lo )

= Ln (1 + (ΔL / L_o ) )

= Ln (1 + e )

True stress, ε = Ln (1 + e )