Question

During a tensile test, a metal has a true strain = 0.08 at a true stress = 37,000 lb/in2. Later, at a true stress = 55,000 lb/in2, true strain = 0.24. Determine the strength coefficient and strain-hardening exponent in the flow curve equation.

Answer 1

The strength coefficient and strain-hardening exponent in the flow curve equation are 92038 and 0.3608.

Step-by-step explanation:

Given that,

True stress = 37000

True strain = 0.08

Later,

True stress = 55000

True strain = 0.24

Using formula of true stress

`\sigma=K\epsilon^n`

We need to make a two equation of true stress

Using formula of true stress

`37000=K(0.08)^n`....(I)

`55000=K(0.24)^n`....(I)

Dividing equation (II) and (I)

`(55000)/(37000)=((0.24)^n)/((0.08)^n)`

`1.4865=((0.24)/(0.08))^n`

`1.4865=3^n`

Taking ln in both side

`ln(1.4865)=n ln(3)`

`n=(ln(1.4865))/(ln(3))`

`n=0.3608`

We need to calculate the value of strength coefficient

Put the value of n in equation (I)

`37000=K(0.08)^(0.3608)`

`K=(37000)/(0.08^(0.3608))`

`K=92038`

Hence, The strength coefficient and strain-hardening exponent in the flow curve equation are 92038 and 0.3608.