Engineering Fundamentals: An Introduction to Engineering
Engineering Fundamentals: An Introduction to Engineering
6th Edition
ISBN: 9780357112311
Author: Saeed Moaveni
Publisher: Cengage Learning US
Question
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Chapter 17, Problem 27P

(a)

To determine

Write the values of modulus of resilience and modulus of toughness for titanium.

The range of modulus of resilience for titanium is 2.888MPato4.167MPa_.

The range of modulus of toughness for titanium is 190.9MPato253MPa_.

(a)

Expert Solution
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Explanation of Solution

Refer Table 17.4 “The strength of Selected Materials” in the textbook.

The range for Yield strength of titanium alloys (σY) is 760MPa1000MPa.

The range for Ultimate strength of titanium alloy (σU) is 900MPa1200MPa.

Refer Table 17.2 “Modulus of Elasticity and Shear Modulus of Selected Materials” in the textbook.

The modulus of elasticity of titanium alloy is E=100GPa120GPa.

The elongation of titanium alloy is 23%.

Find the range of modulus of resilience (Ur) using the relation.

Ur=σY22E (1)

Substitute the minimum and maximum values;

Ur=76022×100GPa×103MPa1GPato100022×120GPa×103MPa1GPa=2.888MPato4.167MPa

Therefore, the range of modulus of resilience is 2.888MPato4.167MPa_.

Find the range of modulus of toughness (Ut) using the relation.

Ut=(σY+σU2)×εf (2)

Substitute minimum and maximum values;

Ut=(760+9002)×0.23to(1000+12002)×0.23=190.9MPato253MPa

Therefore, the range of modulus of toughness is 190.9MPato253MPa_.

(b)

To determine

Write the values of modulus of resilience and modulus of toughness for steel.

The range of modulus of resilience for steel is 0.304MPato2.381MPa_.

The range of modulus of toughness for steel is 66.75MPato165MPa_.

(b)

Expert Solution
Check Mark

Explanation of Solution

Refer Table 17.4 “The strength of Selected Materials” in the textbook.

The range for Yield strength of steel (σY) is 340MPa1000MPa.

The range for Ultimate strength of steel (σU) is 550MPa1200MPa.

Refer Table 17.2 “Modulus of Elasticity and Shear Modulus of Selected Materials” in the textbook.

The range for modulus of elasticity of steel (E) is 190GPa210GPa

The elongation of steel is 15%.

Modulus of resilience:

Substitute the minimum and maximum values in Equation (1).

Ur=34022×190GPa×103MPa1GPato100022×210GPa×103MPa1GPa=0.304MPato2.381MPa

Therefore, the range of modulus of resilience is 0.304MPato2.381MPa_.

Modulus of toughness;

Substitute minimum and maximum values in Equation (2);

Ut=(340+5502)×0.15to(1000+12002)×0.15=66.75MPato165MPa

Therefore, the range of modulus of toughness is 66.75MPato165MPa_.

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