True Stress - True Strain Curve: Part Three

True Stress at Maximum Load

The true stress at maximum load corresponds to the true tensile strength. For most materials necking begins at maximum load at a value of strain where the true stress equals the slope of the flow curve. Let s_u and e_u denote the true stress and true strain at maximum load when the cross-sectional area of the specimen is Au. The ultimate tensile strength is given by

Eliminating P_max yields

(1)

True Fracture Stress

The true fracture stress is the load at fracture divided by the cross-sectional area at fracture. This stress should be corrected for the, triaxial state of stress existing in the tensile specimen at fracture. Since the data required for this correction are often not available, true-fracture-stress values are frequently in error.

True Fracture Strain

The true fracture strain e_f is the true strain based on the original area A₀ and the area after fracture A_f

(2)

This parameter represents the maximum true strain that the material can withstand before fracture and is analogous to the total strain to fracture of the engineering stress-strain curve. Since Eq. (3) is not valid beyond the onset of necking, it is not possible to calculate e_f from measured values of e_f. However, for cylindrical tensile specimens the reduction of area q is related to the true fracture strain by the relationship

(3)

True Uniform Strain

The true uniform strain e_u is the true strain based only on the strain up to maximum load. It may be calculated from either the specimen cross-sectional area A_u or the gage length L_u at maximum load.

Equation (3) may be used to convert conventional uniform strain to true uniform strain. The uniform strain is often useful in estimating the formability of metals from the results of a tension test.

(4)

True Local Necking Strain

The local necking strain e_n is the strain required to deform the specimen from maximum load to fracture.

(5)