QUESHOH 2 The Van Mises yield criterion for a 3D state of stress can be expressed as (I'z = k2 }. (a) Derive an expression for the value of k in terms of o, from the rst principles for a material which has a yield stress = o, in simple tension. Do not use any other pre-derived formula for the yield criterion. (b) If a material has o, = 500 llea is subjected to the threedimensional state of stress given by: 900 250 100 [o]: 250 700 150 MPa 10(] 150 800 Use the result obtained in part (a) to 1. Calculate the equivalent lvlises stress and 2. Determine if yielding will have occurred. ('14 marks} Question 3 An open thin-walled tube, 1000 mm long, has a wall thickness of 2.0 mm and an initial mean diameter of 100 mm. The plastic stressstrain curve for the material is given by (e = 300 20-3 MPa]. The tube is subject to axial load F and internal pressure P, so that the stress ratio owe: = 3.0 at all times. The plastic deformation continues until the mean diameter is increased to 120 mm. Ignoring or Determine: a. The true strain components at the end of the deformation process, b. The equivalent strain at the end of the deformation process, c. The equivalent stress at the end of the defamation process, d. The final dimensions of the tube, 9 The final axial load and internal pressure. Assume that the axial stress in not affected by the internal pressure (open thin-walled tube). ('18 Marks]