1(a) Explain the theories of elastic failure and give their limitations.(6
Marks)

(b) Explain the strain hardening phenomenon. What is the
effect of strain hardening on plastic deformation? (6 Marks)

(c) Explain the Saint-Venant’s theory of plastic flow in
detail. What are the limitations of this theory? (8 Marks)

2(a) Explain the two yield criterias in two-dimensional
applications. (6 Marks)

(b) Derive the Siebel formula for the stress distribution in
the neck of a tensile specimen. (8 Marks)

(c) A tensile test specimen of original diameter 15 mm is
pulled in tension and the following observations are made:

P=150 kN, a=0.6 cm, R=2cm.

Calculate the corrected flow stress at this particular stage
of deformation and the corresponding effective strain. (6 Marks)

3(a) Explain the sand-heap analogy for solving plastic
torsion problems. How this analogy is modified for sections having one or more
holes? What are the limitations of this analogy? (10 Marks)

(b) Write a short note on Tresca’s yield condition. (4
Marks)

(c) A simply supported beam of width 15 cm and depth 20 cm
is 5 m long. It carries two equal loads at 1m from each end. If the yield
stress for the beam material is 225 MPa, draw the residual stress distribution
in the beam if (i) the outer 3 cm shall is to yield, and (ii) the whole of the
beam is to yield. (6 Marks)

4(a) Derive Geiringer’s continuity equations. (8 Marks)

(b) What do you understand by a slip-line? How slip-line
nets can be drawn? (6 Marks)

(c) A solid circular cylinder of radius 20 cm is rotated so
that yielding sets in. Determine the speed of rotation assuming s

_{0}= 150N/mm^{2}, r=7.8 g/cm^{3}(4 Marks)
5(a) What is the role of coefficient of friction in metal
forming? How this can be estimated? (6 Marks)

(b) What is the difference between homogeneous and
non-homogeneous deformation? Explain briefly. (6 Marks)

(c) Derive an equation for the drawing stress at the exit
section with a cylindrical moving mandrel and with back stress applied. (8
Marks)

6(a) Determine and discuss the forces on the rolls of a
four-high rolling mill when the work rolls are driven by the motor. (6 Marks)

(b) Derive an expression for average pressure during closed
die forging with overlapping dies. Modify this expression for axial symmetry.
(7 Marks)

(c) List the advantages of closed-die forgings over open-die
forgings. (4 Marks)

(d) Calculate the bite angle when rolling plates 15mm thick
using work rolls 400 mm diameter and reducing the thickness by 3mm. (3 Marks)

7(a) Derive the expression for the draw stress for tube
sinking with a conical die. (6 Marks)

(b) What is deep drawing? Derive formula to calculate the
radial stress in deep drawing with friction. (8 Marks)

(c) A cylindrical cup without flange is to be drawn from a
2mm thick duralumin sheet. The cup shall have diameter of 15mm and height of
40mm. Reduction ration in first draw and in subsequent draws may not exceed 40%
and 155 respectively. Determine the
blank size and the number of draws necessary. (6 Marks)

8(a) Explain the gas mixture process of metal forming. What
are its characteristics? (4 Marks)

(b) What are the various methods of solving
finite-difference equations? Explain briefly. (6 Marks)

(c) State and prove The Castigliano’s first and second
theorems. (6 Marks)

(d) Write a short note on dynamic plasticity. (4 Marks)

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