Essentials Of Materials Science And Engineering
Essentials Of Materials Science And Engineering
4th Edition
ISBN: 9781337385497
Author: WRIGHT, Wendelin J.
Publisher: Cengage,
Question
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Chapter 17, Problem 17.20P
Interpretation Introduction

Interpretation:

The volume fraction of original compact and volume fraction of closed porosity should be calculated.

Concept introduction:

According to the rules of mixtures for particulate composites:

  ρc=( f i ρ i )for{i=1..........n}ρc=f1ρ1+f2ρ2...................fnρn

Where

  ρc= density of composite

  fi= volume fraction of i component

  ρi= density of i component

Volume fraction is defined as

  f=V1V1+V2f=volumefractionV1=volumeoffirstcomponentV2=volumeofsecondcomponentWhereV1andV2V1=weightoffirstcomponentdensityoffirstcomponentV2=weightofsecondcomponentdensityofsecondcomponentintermsofweightanddensity

  f=V1=weightoffirstcomponentdensityoffirstcomponentV1=weightoffirstcomponentdensityoffirstcomponent+V2=weightofsecondcomponentdensityofsecondcomponent

Expert Solution & Answer
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Answer to Problem 17.20P

The volume fraction of original compact = 0.6006

The volume fraction of closed porosity = 0.0097

Explanation of Solution

Given information:

Weight of tungsten compact = 125gram

Amount of silver infiltered= 105gram

Density of composite = 13.8g/cm3

Based on given information,

Applying rule of mixing:

  ρc=fporeρpore+ftungstenρtungsten+fsilverρsilver..............(A)

  ρc = density of composite is 13.8g/cm3

  fpore = the volume fraction of pore

  ftungsten = the volume fraction of tungsten

  fsilver = the volume fraction of silver

  ρpore = density of porous material is 0

  ρtungsten = density of tungsten

  ρsilver = density of silver

Calculation of volume fraction of tungsten:

  ftungsten=VtungstenVtungsten+Vsilver+Vpore

Volume of tungsten is calculated as:

  Vtungsten=massoftungstendensityoftungstenVtungsten=125gram19.25 gram/cm3Vtungsten=6.493cm3

Volume of silver is calculated as:

  Vsilver=massofsilverdensityofsilverVsilver=105gram10.49 gram/cm3Vsilver=10.009cm3

Substituting the values of volume of silver and volume of tungsten:

  ftungsten=V tungstenV tungsten+V silver+V poreftungsten=6.4936.493+10.009+V poreftungsten=6.49316.502+V pore...................(1)

Calculating volume fraction of silver:

  fsilver=V silverV tungsten+V silver+V porefsilver=10.0096.493+10.009+V porefsilver=10.00916.502+V pore.......................(2)

Calculation of volume fraction for pore:

  fpore=VporeVtungsten+Vsilver+Vpore

  fpore=Vpore6.493+10.009+Vpore

  fpore=Vpore16.502+Vpore...........................(3)

On substituting the values in equation (A),

Values taken are

Density of pore = 0

Density of tungsten = 19.25g/cm3

Density of silver = 10.49g/cm3

  13.8=( V pore 16.502+ V pore )×(0)+( 6.493 16.502+ V pore )×(19.25)+( 10.009 16.502+ V pore )×(10.49)Vpore=0.163cm3

Calculation of volume fraction of original composite:

  foriginalcompact=V silverV totalVtotal=Vsilver+Vtungsten+VporeVtotal=10.009+6.493+0.163Vtotal=16.665cm3

Substituting the value:

  foriginalcompact=10.00916.665foriginalcompact=0.6006

The required value of volume fraction of original compact is 0.6006.

Calculation of volume fraction of closed porosity:

  fclosedporosity=V poreV totalfclosedporosity=0.16316.664fclosedporosity=0.0097

The value of volume fraction for closed porosity = 0.0097.

Conclusion

The volume fraction of original compact = 0.6006

The volume fraction of closed porosity = 0.0097

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