(a)
Interpretation:
Density of composite is to be calculated.
Concept introduction:
Rules of mixtures is:
Where
Volume fraction is defined as:
Answer to Problem 17.29P
The requiredvalue of volume fraction of composite =
Explanation of Solution
Given information:
Weight of boron fiber in unidirectional orientation =
Weight of aluminum fiber in unidirectional orientation =
Based on given information:
Applying rule of mixing,
Calculation of volume fraction of boron is defined as the ratio of volume of boron to total volume:
Calculation of volume of boron, expressed as the ratio of mass of boron to density of boron:
Conversion of mass in gram, therefore multiplying the units by 1000 grams.
Calculation of volume of aluminum:
Calculation of volume fraction of boron and aluminum on substituting the value of volume for boron and aluminum.
Volume fraction of boron = 0.41692
Volume fraction of aluminum = 0.5830
Applying rule of mixing
(b)
Interpretation:
Modulus of elasticity parallel to fiber is to be calculated.
Concept introduction:
Modulus of elasticity is defined as the ratio of shear stress to shear strain.
Relation for modulus of elasticity is given as:
Answer to Problem 17.29P
The required value of modulus of elasticity parallel to fibers is
Explanation of Solution
Calculation of volume fraction of boron is defined as the ratio of volume of boron to total volume:
Calculation of volume of boron, expressed as the ratio of mass of boron to density of boron:
Conversion of mass in gram, therefore multiplying the units by 1000 grams:
Calculation of volume of aluminum:
Calculation of volume fraction of boron and aluminum on substituting the value of volume for boron and aluminum:
Volume fraction of boron = 0.41692
Volume fraction of aluminum = 0.5830
Substituting the following values in the formula of modulus of elasticity:
The required value of modulus of elasticity is 198239.68 MPa.
(c)
Interpretation:
Modulus of elasticity perpendicular to fiber is to be calculated.
Concept introduction:
Modulus of elasticity is defined as the ratio of shear stress to shear strain
Relation for modulus of elasticity perpendicular to fiber is given as:
Answer to Problem 17.29P
The required value of modulus of elasticity perpendicular to fibers is
Explanation of Solution
Calculation of volume fraction of boron is defined as the ratio of volume of boron to total volume:
Calculation of volume of boron, expressed as the ratio of mass of boron to density of boron:
Conversion of mass in gram, therefore multiplying the units by 1000 grams:
Calculation of volume of aluminum:
Calculation of volume fraction of boron and aluminum on substituting the value of volume for boron and aluminum:
Volume fraction of boron = 0.41692
Volume fraction of aluminum = 0.5830
Substituting the following values in the formula of modulus of elasticity
The required value of modulus of elasticity is 104719.40 MPa.
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Chapter 17 Solutions
Essentials Of Materials Science And Engineering
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