Question

Question 4: (A) The ductile behavior of a certain metal is well described by o = 100000€0.3. The metal undergoes uniform work hardening process to a reduction in area of r= 30%, find the yield stress of the work-hardened metal. (5 marks] (B) If the metal in Q4A, governed by the same ductile behavior equation, is cold-worked first by 20% which is still followed by an additional cold work of 15%, find the yield stress of the metal. [10 marks] (C) Provide your comment(s) why the yield stresses in Q4A and Q4B are not the same. (5 marks] [20 marks]

Answer 1

Here, reduction in area is given, this means, strain in area is given. Hence you can calculate the strain in radius.

Note: you cannot directly use 30% as strain, because this is the strain in area. And you have to use the strain in radius (or length) for calculating yield stress.

Now, please refer the image below for detailed solution...

cold New Area New reduced (B) Work Initial cold OH A = 0.8 A Α. (A₂) Area Condition work (A) (Area A) (as there is 20% reduction in area). A2 = 0.85 A1 (as there is 15% reduction in area from stage 1) Az=0-85(0.8A) A₂ = 0.68A * Az = 0.68 o t Az = 1-0.68 & A- Az = 0.32 A (A-A₂) = net reduction in area from initial Condition to final condition. S. (A-A2) = A Anet. AA net = 0.32 SA E Area = 0.32 o Ex- 0-32 = 0.16_ Yield stress o = 100000 (0-16) To=57.708 kPa Answer (C) Due to larger strain in 84B, the yield stress is more in Q4B... oooool As the cold working is done in steps in B4B hence it allows grains of material to accomodate and are settle, thus gaining more Yield stress. 2 0 .3
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