An annealed material with the properties of K 700 MPa and n

An annealed material with the properties of K = 700 MPa and n= 0.2, is initially cold worked some unknown amount. It is then subjected to 15% additional cold work and its yield strength is measured as 525 MPa. What was the unknown amount of cold work induced prior to the 15% added cold work?

Solution

GIVEN:- K = 700 MPa, n = 0.2, %CW2 = 15%, Yield Strength 2 = 525 MPa,

TO FIND:- %CW1 = ?

SOLUTION:- Let initial cross section area be Ao, after some unknown cold work-let it be A1 and after 15% cold work-let it be A2

%CW2 = (A1 - A2) / A1 x 100 = 15 i.e. A1 = 1.18 x A2 ---- Equation > 1

%CW1 = (A0 - A1) / A0 x 100 = ?    -----Equation > 2

2 = 525 = F / A2, so A2 = F / 525 -----Equation > 3

Since F = load remains constant, A1 = F / 1 = 1.18 (F / 525) (From Eq-1 and Eq-3)

i.e. 1 = 445 MPa and 1 for this value = 0.10 (by relation = K x ^n )

Similarly 2 = 525 MPa and 2 for this value = 0.23

So 0 will be 0, so 0 = 0 This means F / A0 = 0 = 0

So from equation - 2, we get %CW1 = (0 - A1) / 0 x 100 = 0 % (ANSWER)