196. The true stress (σ), true strain (ε) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e. up to stress of 500 MPa and strain of 0.5. then from point A, there is unloading up to point B, i.e. to stress of 100 MPa, Given that the Young's modulus E = 200 GPa, the natural strain at point B (ε_B) _____(correct to two decimal places).
     

1. 1. 0.498

   
   
   

   2. - 0.498

   
   
   

   3. - 1.498

   
   
   

   4. 1.498

   
   
   

---

1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

---

197. The maximum reduction in cross-sectional area per pass (R) of a cold wire drawing process is R = 1 – e^{–(n + 1)} where n represents the strain hardening coefficient. For the case of a perfectly plastic material, R is

1. 1. 0.865

   
   
   

   2. 0.826

   
   
   

   3. 0.777

   
   
   

   4. 0.632

   
   
   

---

1. View Hint View Answer Discuss in Forum

   σ_d = σ₀ l n .
   For Maximum Reduction
   σ_d = σ₀.
   

   l = ln			Ai
   			Af

   
   R = 0.63

   Correct Option: D

   σ_d = σ₀ l n .
   For Maximum Reduction
   σ_d = σ₀.
   

   l = ln			Ai
   			Af

   
   R = 0.63

---

---

198. A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is (correct to two decimal places).

1. 1. - 0.6932

   
   
   

   2. - 1.6932

   
   
   

   3. 0.6932

   
   
   

   4. 1.6932

   
   
   

---

1. View Hint View Answer Discuss in Forum

   ∈T = ln			lf			²
   			li

   
   
   

   Correct Option: A

   ∈T = ln			lf			²
   			li

   
   
   

---

199. In a two-stage wire drawing operation, the fractional reduction (ratio of change in crosssectional area to initial cross-sectional area) in the first stage is 0.4. The fractional reduction in the second stage is 0.3. The overall fractional reduction is

1. 1. 0.24

   
   
   

   2. 0.58

   
   
   

   3. 0.60

   
   
   

   4. 1.00

   
   
   

---

1. View Hint View Answer Discuss in Forum

   40% Reduction = 1 × 0.4 = 0.4
   30% Reduction of 0.6 = 0.6 × 0.3 = 0.18
   Total Reduction = 0.58

   Correct Option: B

   40% Reduction = 1 × 0.4 = 0.4
   30% Reduction of 0.6 = 0.6 × 0.3 = 0.18
   Total Reduction = 0.58

---

---

200. A metal rod of initial length L0 is subjected to a drawing process. The length of the rod at any instant is given by the expression, L(t) = L₀ (1 + t²), where t is the time in minutes. The true strain rate (in min^–1) at the end of one minute is _______.

1. 1. 1 min^–1

   
   
   

   2. 2 min^–1

   
   
   

   3. 3 min^–1

   
   
   

   4. 4 min^–1

   
   
   

---

1. View Hint View Answer Discuss in Forum

   L(t) = L₀ (1 + t²)
   ⇒ dL = L₀ × 2t dt
   

   As d ∈T =	dL
   	L

   
   

   d ∈T =	L02t dt
   	L0 (1 + t²)

   
   

   		d ∈T	=	2t
   		dt		1 + t²

   
   at t = 1 min
   

   		∈T	=	2 × 1	= 1 min- 1
   		T		1 + 1²

   
   

   Correct Option: A

   L(t) = L₀ (1 + t²)
   ⇒ dL = L₀ × 2t dt
   

   As d ∈T =	dL
   	L

   
   

   d ∈T =	L02t dt
   	L0 (1 + t²)

   
   

   		d ∈T	=	2t
   		dt		1 + t²

   
   at t = 1 min
   

   		∈T	=	2 × 1	= 1 min- 1
   		T		1 + 1²

   
   

---