Essentials Of Materials Science And Engineering
Essentials Of Materials Science And Engineering
4th Edition
ISBN: 9781337670845
Author: ASKELAND
Publisher: Cengage
Question
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Chapter 8, Problem 8.10P
Interpretation Introduction

Interpretation:

The strain-hardening exponent for the metal needs to be determined. Whether the metal is FCC, BCC or HCP needs to be explained.

Concept introduction:

Strain hardening is called work hardening. Strengthening occurs due to plastic deformation. Strengthening occurs due to dislocation movement.

Expert Solution & Answer
Check Mark

Answer to Problem 8.10P

Strain hardening exponent for the metal 'n' is 0.12. The value of strain hardening is in BCC metals.

Explanation of Solution

Given Information:

The measurements in the plastic regions are as follows:

Force (1b)Change in gage length (in)   (Δ1)Diameter (in)
27,5000.21030.4800
27,0000.44280.4566
25,7000.69970.4343

Calculation:

Now, stress acting on the metal bar at 27500 lb

  σ1=fd1Af --------------- (1)

But

  Af=πFdi2=areaofbar

Where,

  Fd1=Force of metal bar=27500lbd1=Diameter of bar=0.48in.

Equation (1) becomes,

  σ1=27500π4× 0.482σ1=151970Psi

Now, stress acting at

  kd2=27000lb,d2=0.4566inσ2=fd2A2σ2=fd2π4d22σ2=27000π4× 0.45662σ2=164893Psi

At,

  kd3=27000lb,d3=0.4343inσ3=257000π4× 0.43432σ3=173486Psi

Calculating 'n' for force 27500 lb act on metal by using formula.

  σ1=kξ1nlnσ1lnk+nlnξ --------------- (2)

Where,

  ξ=true strain=0.1σ1=27500lb

Equation (2) becomes,

  ln(151970)=lnk+nln(0.1)11.9314=lnk+n(2.3026) --------------------- (a)

Now,the force of 25700 lb act on metal, strain hardening is given by,

  σ3=kξ3n

Applying logarithm on both sides

  lnσ3lnk+nlnξ

Here,

  ξ=True strain=0.3σ3=Stress acting=25700lb 

Equation (3) becomes,

  ln(173486)=lnk+nln(0.3)12.0636=lnk+n(1.2040) ---------------- (b)

From equation (a) and (b),

  n=0.12

Conclusion

Thus, strain hardening exponent for metal 0.12 which is in BCC range.

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Chapter 8 Solutions

Essentials Of Materials Science And Engineering

Ch. 8 - Prob. 8.11PCh. 8 - Prob. 8.12PCh. 8 - Prob. 8.13PCh. 8 - Prob. 8.14PCh. 8 - Prob. 8.15PCh. 8 - Prob. 8.16PCh. 8 - Prob. 8.17PCh. 8 - Prob. 8.18PCh. 8 - Prob. 8.19PCh. 8 - Prob. 8.20PCh. 8 - Prob. 8.21PCh. 8 - Prob. 8.22PCh. 8 - Prob. 8.23PCh. 8 - Prob. 8.24PCh. 8 - Prob. 8.25PCh. 8 - Prob. 8.26PCh. 8 - Prob. 8.27PCh. 8 - Prob. 8.28PCh. 8 - Prob. 8.29PCh. 8 - Prob. 8.30PCh. 8 - Prob. 8.31PCh. 8 - Prob. 8.32PCh. 8 - Prob. 8.33PCh. 8 - Prob. 8.34PCh. 8 - Prob. 8.35PCh. 8 - Prob. 8.36PCh. 8 - Prob. 8.37PCh. 8 - Prob. 8.38PCh. 8 - Prob. 8.39PCh. 8 - Prob. 8.40PCh. 8 - Prob. 8.41PCh. 8 - Prob. 8.42PCh. 8 - Prob. 8.43PCh. 8 - Prob. 8.44PCh. 8 - Prob. 8.45PCh. 8 - Prob. 8.46PCh. 8 - Prob. 8.47PCh. 8 - Prob. 8.48PCh. 8 - Prob. 8.49PCh. 8 - Prob. 8.50PCh. 8 - Prob. 8.51PCh. 8 - Prob. 8.52PCh. 8 - Prob. 8.53PCh. 8 - Prob. 8.54PCh. 8 - Prob. 8.55PCh. 8 - Prob. 8.56PCh. 8 - Prob. 8.57PCh. 8 - Prob. 8.58PCh. 8 - Prob. 8.59PCh. 8 - Prob. 8.60PCh. 8 - Prob. 8.61PCh. 8 - Prob. 8.62PCh. 8 - Prob. 8.63PCh. 8 - Prob. 8.64PCh. 8 - Prob. 8.65PCh. 8 - Prob. 8.66PCh. 8 - Prob. 8.67PCh. 8 - Prob. 8.68PCh. 8 - Prob. 8.69PCh. 8 - Prob. 8.70PCh. 8 - Prob. 8.71PCh. 8 - Prob. 8.72PCh. 8 - Prob. 8.73PCh. 8 - Prob. 8.74PCh. 8 - Prob. 8.75PCh. 8 - Prob. 8.76PCh. 8 - Prob. 8.77PCh. 8 - Prob. 8.78PCh. 8 - Prob. 8.79PCh. 8 - Prob. 8.80PCh. 8 - Prob. 8.81PCh. 8 - Prob. 8.82PCh. 8 - Prob. 8.83PCh. 8 - Prob. 8.84PCh. 8 - Prob. 8.85PCh. 8 - Prob. 8.86PCh. 8 - Prob. 8.87DPCh. 8 - Prob. 8.88DPCh. 8 - Prob. 8.89DPCh. 8 - Prob. 8.90CPCh. 8 - Prob. K8.1KP
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