@Dinesh: Ok I wants to say that I am not too good in this Forming section but still I will try to solve this; Lets see how much can I help you !!!
Say, Original c/s Area = O.A.
Final c/s Area = F.A.
Area After First Die = A1
Original Length = O.L.
Final Length = F.L.
Now O.A. = (pi/4)*(10^2) = 78.5398 mm2
A1 = (1-0.35)*(O.A.) = 0.65*(O.A.) = 51.0508 mm2
Similarly for the area after 7th die
= 0.65*0.65*0.65*0.65*0.65*0.65*0.65*(O.A.) … .. (For 7 dies)
= (0.65)^7 * (O.A.)
= 3.8502 mm2 = F.A.
Now, as True strain is instantaneous % of change in length of specimen & it is given by,
True strain (TS) = Natural log of (O.A./F.A.)
= ln (78.5398/3.8502)
= 3.0155 ———————————–ANS
Final length can be calculated by using constant volume principle as,
Initial Volume = Final Volume
(O.A.)*(O.L.) = (F.A.)*(F.L.)
78.5398 * 100 = 3.8502 * F.L.
F.L. = 2039.8888
= 2040 mm ————————————-ANS
Now, For force we have to calculate a Draw Stress after first die,
using uniform energy deformation method,
Draw Stress (D.S.) = Y * ln(O.A./A1) …… … (Y = Yield Strength)
(Note this formula can be used for only Ideal Conditions i.e. neglecting friction and redundant work)
Hence, D.S. = 200 * ln (78.5398/51.0508)
= 86.1568 N/mm2
Now, Drawing Force through first die is,
Drawing Force (F) = (D.S.)*(A1)
= 86.1568 * 51.0508
= 4398.3735 N
= 4.4 kN ———————————ANS
Note: Please check the answers & do notify in reply. If possible then mention the answers (options) along with the questions.
@Dinesh: Ok I wants to say that I am not too good in this Forming section but still I will try to solve this; Lets see how much can I help you !!!
Say, Original c/s Area = O.A.
Final c/s Area = F.A.
Area After First Die = A1
Original Length = O.L.
Final Length = F.L.
Now O.A. = (pi/4)*(10^2) = 78.5398 mm2
A1 = (1-0.35)*(O.A.) = 0.65*(O.A.) = 51.0508 mm2
Similarly for the area after 7th die
= 0.65*0.65*0.65*0.65*0.65*0.65*0.65*(O.A.) … .. (For 7 dies)
= (0.65)^7 * (O.A.)
= 3.8502 mm2 = F.A.
Now, as True strain is instantaneous % of change in length of specimen & it is given by,
True strain (TS) = Natural log of (O.A./F.A.)
= ln (78.5398/3.8502)
= 3.0155 ———————————–ANS
Final length can be calculated by using constant volume principle as,
Initial Volume = Final Volume
(O.A.)*(O.L.) = (F.A.)*(F.L.)
78.5398 * 100 = 3.8502 * F.L.
F.L. = 2039.8888
= 2040 mm ————————————-ANS
Now, For force we have to calculate a Draw Stress after first die,
using uniform energy deformation method,
Draw Stress (D.S.) = Y * ln(O.A./A1) …… … (Y = Yield Strength)
(Note this formula can be used for only Ideal Conditions i.e. neglecting friction and redundant work)
Hence, D.S. = 200 * ln (78.5398/51.0508)
= 86.1568 N/mm2
Now, Drawing Force through first die is,
Drawing Force (F) = (D.S.)*(A1)
= 86.1568 * 51.0508
= 4398.3735 N
= 4.4 kN ———————————ANS
Note: Please check the answers & do notify in reply. If possible then mention the answers (options) along with the questions.