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November 1st, 2018, 01:40 AM   #1
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Homogenous stress/strain

Hi all,

Any help would be appreciated.

A fibre-reinforced composite has 25% volume of carbon fibres with a modulus of elasticity of 150.0 GPa. The remaining matrix material is polyester resin with a modulus of elasticity of 3.10 GPa.

Use the homogeneous strain (parallel) model, to calculate an upper limit for the effective Young’s modulus of this composite material. Give your answer to three significant figures.


Use the homogeneous stress (series) model to calculate a lower limit for the effective Young’s modulus of this composite material. Give your answer to three significant figures.


Based on your calculations in the above questions, suggest two key engineering considerations for the use of unidirectional fibre-reinforced composites in the design of load-bearing engineering structures.

You can assume that the homogeneous strain (parallel) model applies when the load is applied parallel to the direction of orientation of the fibres in the composite, and that the homogeneous stress (series) model applies when the load is applied perpendicular to the direction of orientation of the fibres.

Thanks.

Last edited by skipjack; November 1st, 2018 at 03:21 AM.
NAC54321 is offline  
 
November 1st, 2018, 02:04 AM   #2
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Math Focus: Yet to find out.
You just posted this three times.

[Note by moderator: one copy suffices, so I've removed the other two.]

Last edited by skipjack; November 1st, 2018 at 03:23 AM.
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November 1st, 2018, 04:08 PM   #3
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You have just posted your homework, what do you expect us to do?

I don't do people's homework for them but the following sketch may help.

The first situation shows the conditions pertaining when the fibres are arranged longitudinally and transversally in a bar. This put the longitudinal fibres in parallel strain with the matrix.

The second shows transverse fibres which generate a series strain.

Note the conditions refer to the loads and extensions, from which the stresses and strains may be obtained via the appropriate areas and elasticity constants.


Ask again if you need more help.
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November 13th, 2018, 06:09 AM   #4
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Thanks for your help studiot only now seeing this.

It is a quiz question which will aid me in my final exam, I don't know where to start with it that's why I asked for some help.
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November 13th, 2018, 08:41 AM   #5
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Hi Studiot,

Do you agree with my calculation below?

(3.10 x 0.75) x (150 x 0.25)
= (37.5) x (2.325)
= 39.825 GPa.
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