Manufacturing Processes for Engineering Materials (6th Edition)
Manufacturing Processes for Engineering Materials (6th Edition)
6th Edition
ISBN: 9780134290553
Author: Serope Kalpakjian, Steven Schmid
Publisher: PEARSON
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Chapter 3, Problem 3.43P

(a)

To determine

The theoretical shear strength for aluminum, plain-carbon steel, and tungsten.

(a)

Expert Solution
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Answer to Problem 3.43P

The theoretical shear strength for aluminum, plain-carbon steel, and tungsten are 4.69GPa , 11.96GPa , and 25.06GPa respectively.

Explanation of Solution

Formula used:

The expression for the modulus of rigidity is given as,

  G=E2(1+v)

Here, E is the young’s modulus, and v is the Poisson’s ratio.

The expression for the theoretical shear strength is given as,

  (τtheo)=(G)2π

Calculation:

The value of Young’s modulus and Poisson’s ratio for aluminum is,

  (E)Al=79GPav=0.34

The value of modulus of rigidity of aluminum can be calculated as,

  (G)Al= ( E ) Al2( 1+v)=79GPa2( 1+0.34)=29.47GPa

The value of Young’s modulus and Poisson’s ratio for steel is,

  (E)steel=200GPav=0.33

The value of modulus of rigidity of steel can be calculated as,

  (G)steel= ( E ) steel2( 1+v)=200GPa2( 1+0.33)=75.18GPa

The value of Young’s modulus and Poisson’s ratio for tungsten is,

  (E)W=400GPav=0.27

The value of modulus of rigidity of tungsten can be calculated as,

  (G)W= ( E )W2( 1+v)=400GPa2( 1+0.27)=157.48GPa

The value of theoretical shear strength of aluminum can be calculated as,

  ( τ theo)Al= ( G ) Al2π=29.47GPa2π=4.69GPa

The value of theoretical shear strength of steel can be calculated as,

  ( τ theo)steel= ( G ) steel2π=75.18GPa2π=11.96GPa

The value of theoretical shear strength of tungsten can be calculated as,

  ( τ theo)W= ( G )W2π=157.48GPa2π=25.06GPa

Conclusion:

Therefore, the theoretical shear strength for aluminum, plain-carbon steel, and tungsten are 4.69GPa , 11.96GPa , and 25.06GPa respectively.

(b)

To determine

The theoretical tensile strength for aluminum, plain-carbon steel, and tungsten.

The ratios of their theoretical strength to actual strength.

(b)

Expert Solution
Check Mark

Answer to Problem 3.43P

The theoretical tensile strength for aluminum, plain-carbon steel, and tungsten are 7.9GPa , 20GPa , and 40GPa respectively.

The ratios of theoretical strength to actual strength of aluminum, plain-carbon steel, and tungsten are 0.87 , 0.8 , and 0.95 respectively.

Explanation of Solution

Formula used:

The expression for the theoretical tensile strength is given as,

  σtheo=E10

The expression for the ratio of theoretical tensile strength to actual tensile strength is given as,

  R=(σ theo)(σ actual)

Here, (σactual) is the actual tensile strength.

Calculation:

The value of theoretical tensile strength of aluminum can be calculated as,

  ( σ theo)Al= ( E ) Al10=79GPa10=7.9GPa

The value of theoretical tensile strength of steel can be calculated as,

  ( σ theo)steel= ( E ) steel10=200GPa10=20GPa

The value of theoretical tensile strength of tungsten can be calculated as,

  ( σ theo)W= ( E )W10=400GPa10=40GPa

The actual tensile strength of the aluminum is,

  (σ actual)Al=9GPa

The actual tensile strength of the steel is,

  (σ actual)steel=25GPa

The actual tensile strength of the steel is,

  (σ actual)W=42GPa

The value of the ratio of theoretical tensile strength to actual tensile strength for aluminum can be calculated as,

  RAl= ( σ theo ) Al ( σ actual ) Al=7.9GPa9GPa=0.87

The value of the ratio of theoretical tensile strength to actual tensile strength for steel can be calculated as,

  Rsteel= ( σ theo ) steel ( σ actual ) steel=20GPa25GPa=0.8

The value of the ratio of theoretical tensile strength to actual tensile strength for tungsten can be calculated as,

  RW= ( σ theo )W ( σ actual )W=40GPa42GPa=0.95

Conclusion:

Therefore, the theoretical tensile strength for aluminum, plain-carbon steel, and tungsten are 7.9GPa , 20GPa , and 40GPa respectively.

Therefore, the ratios of theoretical strength to actual strength of aluminum, plain-carbon steel, and tungsten are 0.87 , 0.8 , and 0.95 respectively.

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