Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
Question
Book Icon
Chapter 12, Problem 12.14P

(a)

To determine

The strain in composite when stress in matrix is 60 MPa .

(a)

Expert Solution
Check Mark

Answer to Problem 12.14P

The strain in composite when stress in matrix reaches 60 MPa is 0.025.

Explanation of Solution

Given:

Elastic modulus of polycarbonate matrix is 2.4×109 Pa .

Maximum allowable stress in matrix is 60 MPa .

Concept used:

Write the expression for strain in composite.

  εC=σmEm …… (1)

Here, εC is the strain in composite, σm is the stress in matrix and Em is the elastic modulus of matrix.

Calculation:

Substitute 60 MPa for σm and 2.4×109 Pa for Em in equation (1).

  εC=60 MPa( 10 6 Pa 1MPa )2.4× 109 Pa=0.025

Conclusion:

Thus, the strain in composite when stress in matrix reaches 60 MPa is 0.025.

(b)

To determine

The fiber stress for continuous fiber composite and identify if this is less than tensile strength of fiber.

(b)

Expert Solution
Check Mark

Answer to Problem 12.14P

The fiber stress for continuous fiber composite is 3.25 GPa this is close to tensile strength of fiber.

Explanation of Solution

Given:

Elastic modulus of Fiber is 130×109 Pa .

Concept used:

Write the expression for fiber stress.

  σf=εCEf …… (2)

Here, σf is the fiber stress and Ef is the modulus of elasticity of fiber.

Calculation:

Substitute 0.025 for εC and 130×109 Pa for Ef in equation (2).

  σf=(0.025)(130× 109 Pa)=3.25×109 Pa( 1 GPa 10 9  Pa)=3.25 GPa

Conclusion:

Thus, the fiber stress for continuous fiber composite is 3.25 GPa this is close to tensile strength of fiber.

(c)

To determine

Critical fiber length

(c)

Expert Solution
Check Mark

Answer to Problem 12.14P

Critical fiber length is 6.1×104m .

Explanation of Solution

Given:

Diameter of aramid fiber is 12×106 m .

Shear strength of Polycarbonate-aramid interface is 32×106 Pa .

Concept used:

Write the expression for critical aspect ratio.

  lCdf=σf2τmf* …… (3)

Here, lC is the critical fiber length, df is the diameter of fiber and τmf* is the maximum shear stress in interface.

Calculation:

Substitute 12×106 m for df , 32×106 Pa for τfm* and 3.25 GPa for σf in equation (3).

  lC12× 10 6 m=3.25 GPa( 10 9  Pa 1 GPa )2( 32× 10 6  Pa)lC=6.1×104m

Conclusion:

Thus, the Critical fiber length is 6.1×104m .

(d)

To determine

Average stress in chopped aramid fiber.

(d)

Expert Solution
Check Mark

Answer to Problem 12.14P

Average stress in chopped aramid fiber is 1.6 GPa .

Explanation of Solution

Given:

Length of aramid fiber is 6×104 m .

Concept used:

Write the expression for average fiber stress.

  σ¯f=σf(1lC2l) …… (4)

Here, σf¯ is the average fiber stress and l is the length of fiber.

Calculation:

Substitute 3.25 GPa for σf , 6.1×104m for lC and 6×104 m for l in equation (4).

  σ¯f=3.25 GPa(1 6.1× 10 4  m 2( 6× 10 4  m ))=1.6 GPa

Conclusion:

Thus, the average stress in chopped aramid fiber is 1.6 GPa .

(e)

To determine

Composite material stress.

(e)

Expert Solution
Check Mark

Answer to Problem 12.14P

Composite material stress is 753 MPa .

Explanation of Solution

Given:

Volume percentage of aramid chopped fiber is 45% .

Volume percent of polycarbonate matrix is 55% .

Tensile strength of aramid fiber is 3.6×109 Pa .

Tensile strength of Polycarbonate is 80 MPa .

Concept used:

Write the expression for composite material stress.

  σC=Vfσ¯f+Vmσm …… (5)

Here, σC is the composite material stress, Vf is the volume fraction of fiber and Vm is the volume fraction of matrix.

Calculation:

Substitute 0.45 for Vf , 0.55 for Vm , 1.6 GPa for σ¯f and 60 MPa for σm in equation (5).

  σC=(0.45)(1.6 GPa)( 10 9  Pa 1 GPa)+(0.55)(60 MPa)( 1 0 6  Pa 1 MPa)=720×106 Pa+33×106 Pa=753×106 Pa( 1 MPa 10 6  Pa)=753 MPa

Conclusion:

Thus, the composite material stress is 753 MPa .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A composite sample of carbon reinforced epoxy has dimensions of in 20 in x 20 in x 0.135 in and mass of 3 lb. The carbon fibres have a modulus of elasticity of 80(106) lb/in2 and a density of 0.15 lb/in3. The epoxy matrix has modulus of elasticity of 0.90(106) lb/in2 and a density of 0.05 lb/in3.  Assume there are no voids in the sample, calculate the volume fraction of: (i) The carbon fibres (ii) The epoxy matrix in the sample.
A steel bar and an aluminum bar are bonded together as shown to form a composite beam. Knowing that the vertical shear in the beam is 4 kips and that the modulus of elasticity is 29 * 106 psi for the steel and 10.6 *106 psi for the aluminum, determine (a) the aver-age shearing stress at the bonded surface, (b) the maximum shearing stress in the beam.
The composite bar is initially stress-free. Calculate the stress in each material and indicate tension or compression if the temperature has increased to 25°C. Consider that the walls are unyielding and suitably braced to prevent buckling. Use 2 decimal places.
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Materials Science And Engineering Properties
Civil Engineering
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Cengage Learning