How the composite fails under load?

1
How the composite fails under load?

• Consider the case in which a tensile stress
  acts parallel to the fibre (axis 1).
•  
• Fig. Fig.
•  
• Case 1 Ef lt Em
•  
• The mode of failure depend on Ef and Em.
•  
• Mode (1) is brittle fibres inductile matrix.
• Mode (2) is dectile fibres in brittle matrix.
•  

2

• Example of this mode is epoxy resin reinforced
  by carbon fibre.
• Asssume a parallel coupling between fibres and
  matrix for stress parallel to axis 1.
• Also assume that fibres and matrix in the
  composite are to fail independently, at the
  same stresses and strains as when tensile tests
  are carried out on the pure material.
•  
• As strain is increased, a point is reached
  around Ef where fibre begin to break, and their
  contribution to the total stress falls to zero.

3

• The second step depends on ?f (1) at low ?f
•  
• There is sufficient matrix to carry the tensile
  load even after all fibre have fialed.
• And
• The total stress at strain E1 is, from now on,
  Just the contribution of the matrix alone
  
• (1-?f) ?m
•  
• Finally (with further straining)
•  
• The composite fails when the matrix which
  contain brokken fibres fails at E1 Em.

4
For high ?f

• When the fibres break there is insufficient
  matrix to maintain the same stress
•  
• Thus the point of failure of the fibres then
  marks the failure of the composite also
•  
• In this case the stress just prior to failure
  is the sum of ?f?f and (1- ?f ) ?m
•  
• where ?m ?m (Ef). The stress carried by the
  matrix at the failure strain of the fibres.

5
? Summary

• Low ?f ?1 (1 - ?f ) ?m (2.26a)
• high ?f ?1 ?f?f (1- ?f) ?m (2.26b)

6
How to calculate the minimum volume fraction of
reinforcement.

• Equations (2.26) give two estimates for ?1 as
  shown in the figure
•  
•  
• Fig.
•  
•  
• Except at vary low fibre fractions tensile
  strength is dominated by the contribution
• from the fibres. ?1 ? ?f?f
• Thus
• A minimum fibre fraction is required before
  the fibre exert a strengthening effect at all.
•  
• Lower values of ?2 will result is weakening
  the matrix and must be avoided.
• Therefore
• ?fmin is a critical parameter.
• ?fmin is obtained by equating ---- with
  ---- from equation (2.26b)
•  

7
Example 6.
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Thank You

• See You Next Lecture