Materials Science and Engineering: An Introduction, 10e WileyPLUS + Abridged Loose-leaf
Materials Science and Engineering: An Introduction, 10e WileyPLUS + Abridged Loose-leaf
10th Edition
ISBN: 9781119472070
Author: William D. Callister Jr., David G. Rethwisch
Publisher: Wiley (WileyPLUS Products)
Question
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Chapter 8, Problem 1QAP
To determine

The maximum stress (σm) that can be present at the tip of an internal crack.

Expert Solution & Answer
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Answer to Problem 1QAP

Maximum stress (σm) at the tip of an internal crack is 2404MPa .

Explanation of Solution

Given:

The Radius of Curvature of the internal crack tip, ρt=2.5×104mm .

Length of the internal Crack =2.5×102mm .

Tensile Strength Applied, σ0=170MPa .

Formula used:

The maximum stress at the tip of the crack can be calculated by the formula :

  σm=2σ0aρt12

where σm= Maximum Stress

  σ0= Tensile Strength

  a= Length of the surface Crack

  ρt= Radius of Curvature of the internal crack tip

Calculation:

To calculate the maximum stress at the tip of the crack, first find out the length of the surface crack :

  a=2.5×1022mma=1.25×102mm

Now, using the formula :

  σm=2σ0aρt12σm=2×170MPa1.25×102mm2.5×104mm12σm=3405012MPaσm=340×7.07MPaσm=2403.8MPa2404MPa

Conclusion:

The magnitude of the maximum stress (σm) at the tip of an internal crack is 2404MPa .

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