Question 1. A thin-walled tube, 300 mm long, has a wall thickness of 1.0 mm and an initial mean diameter of 120 mm. The plastic stress-strain curve for the material is given by ( σ = 500 ε 0.25 MPa). The tube is subject to axial load F and internal pressure p so that the stress ratio σθ/σz = 3.0 at all times. The deformation continues until the effective stress equals 200 MPa. Ignoring σr determine:

a) the effective strain at the end of the deformation process

b) the true strain components at the end of the deformation process

c) the final dimensions of the tube

d) the final axial load and internal pressure.

Assume that the axial stress in not affected by the internal pressure.

Question 2. A short cylindrical billet 16 mm diameter and 40 mm gauge length is elongated under tensile load to 50 mm and then compressed to 30 mm. The material characteristic curve under axial loading is given by (σ = 300 ε 0.4 MPa). Ignoring the elastic deformations and Bauschinger effect, determine:

a) the diameter of the billet after elongation,

b) the final diameter of the billet after recompression,

c) the equivalent strain and new yield stress of the elongated billet,

d) the final equivalent strain and the yield stress after recompression to 30 mm,

e) the force required to elongate the billet to 50 mm,

f) the force needed to recompress the billet back to 30 mm.

Question 3 A plate of mild steel, 10 mm thick, 1000 mm long and 500 mm wide is stretched plastically 25% in the longitudinal direction. The characteristic stress-strain curve of the material is given by (σ = 500 ε 0.4 MPa). Assuming that the width is restrained from contracting by lateral end grips, calculate:

a) final dimensions of the plate

b) state of stress at the end of the stretching process

c) final stretching load.