Given that the true strain at the onset of necking is numeri

Given that the true strain at the onset of necking is numerically equal to the strain-hardening exponent of a material. Assume that a given material has a true stress-true strain curve given by; sigma = 100,000e^0.5 Calculate the true ultimate tensile strength of the material. Calculate the engineering ultimate tensile strength of the material.

Solution

GIVEN DATA: STRESS=100000e^0.5 Since strain at onset of backing e=n=0.5 .......hence STRESS=Knⁿ=100000×0.5^0.5=70710 psi....True area at onset of necking is ln (A_o/A_neck)=n=0.5 so A_neck = A_o e-0.5 (e^-0.5=0.606) Maxium load P=STRESS × Area = STRESS × A_neck=Stress × A_oe^-0.5   Engineering UTS = P/A_o = 70710×0.606×A_o/A_o   Engieering UTS= 42,850 psi. TRUE UTS = ENGINEERING UTS/(e+1)=42850/(0.5+1)=28566.67 psi.