1. Subject: Composite Materials Science and Engineering Subject code: 0210080060
Prof C. H. XU
School of Materials Science and Engineering
Henan University of Science and Technology
Chapter 9:
Mechanical Properties of Composites

2. Chapter 9: Mechanical Properties of Composites -Introduction
The methods of calculating the stiffness and strength of composites
Based on the orientation of reinforcement, the properties of a composite can be
Isotropic (各向同性）:
composites with the random orientation of reinforcement, such as sort fibers or particles
Anisotropic (各向异性）:
continuous fiber composites,
Lamellar composites
Skin-Core-Skin pattern
Some composite with short fibers (pressure molded short fiber composites)
This chapter introduces the calculation of stiffness and strength of the composite fiber-reinforced or lamellar composites at special directions.

3. Mechanical Property - Fiber-reinforced or lamellar composites
Volume fraction of matrix
Volume fraction of reinforcement

4. Mechanical Property - Fiber-reinforced or lamellar composites
Heterogeneity (异质)
Composites’ properties and structures vary from point to point.
Property relationship
The properties of a composite are determined largely by
properties of the constituents,
their relative concentration,
their geometric arrangement and
the nature of the interface between them.
Anisotropy
the strength and stiffness are highest in the direction of fibre orientation, but are week in the direction of the transverse direction.

5. Deformation
The mechanical characteristics of a
fiber-reinforced composite depend
on the properties of the fiber and
on the degree of load transmittance to
the matrix phase.
Important to the degree of this load
transmittance is the magnitude of
the interfacial bond between the
fiber and matrix phases.
Under an applied stress, this fiber-
matrix bond ceases at the fiber ends.

7. Fiber-reinforced Composites

8. Fiber-reinforced Composites

9. Fiber-reinforced Composites
Influence of Fiber Orientation and Concentration
Two extremes: (a) a parallel alignment of the longitudinal axis of the fibers in a single direction; and (c) a totally random alignment.

10. Continuous and aligned fiber composites
Tensile stress-strain behavior depends on the fiber and matrix phases; the phase volume fractions; the direction of loading.
with longitudinal loading
in stage I, both fiber and matrix deform elastically.
in stage II, the fiber continues to deform elastically, but the matrix has yielded.
from stage I to II, the fiber picks up more load.
the onset of composite failure begins as the fibers start to fracture.
composite failure is not catastrophic.

11. ec = ef = em Fiber-reinforced Composites
- Continuous and Aligned Fibre Composites
Longitudinal Loading
The properties of a composite depend on the
fibre direction.
Assuming the fiber-matrix interfacial bond is
very good, such that
deformation of both
matrix and fibers is the same (Isostrain) .
ec = ef = em

12. Fiber-reinforced Composites

13. Fiber-reinforced Composites
Using Volume Fraction: V
= V /V = A /A
: the volume m
vol,m
vol,c m c
fractions of the matrix V
= V /V = A /A
: the volume fractions f
vol,f
vol,c f c
of the fiber
The composite stress becomes: f m c V s + =

14. Fiber-reinforced Composites

15. The modulus of elasticity of a continuous and aligned fibrous composite in the direction of alignment (or longitudinal direction): Ecl E V cl m f = + 1 - ( )
Rule of Mixture
is equal to the volume-
fraction weighted average 加权平均值 of
the
moduli of elasticity of the
fiber and matrix phases.

16. Students can give this equation. (TS)lc= ?
·     Other properties, including tensile strength, also have this dependence on volume fractions.
Students can give this equation.
(TS)lc= ?
It can also be shown, for longitudinal loading, that the ratio of the load carried by the fibers to that carried by the matrix is

17. Fiber-reinforced Composites

18. Rule of Mixture

19. Fiber-reinforced Composites Discontinuous and aligned fiber composites
Moduli of elasticity and tensile strengths of short fiber composites are about % these of long fiber composites.
When l > lc, the longitudinal strength (TS)cd
Where (TS)f is the fracture strength of the fiber and (TS)’m is the stress in the matrix when the composite fails.
When l < lc, the longitudinal strength is
Where d is the fiber diameter and c is the shear yields strength of the matrix.

20. Fiber-reinforced Composites Discontinuous and randomly oriented composites
The orientation of the short and discontinuous fibers is random in matrix.
A ‘rule-of-mixtures’ expression for the elastic modulus Ecd
where K is a fiber efficiency parameter depended on Vf and Ef/Em ratio (0.1 ~ 0.6)

21. A continuous and aligned glass-reinforced composite consists of
Example Problem:
A continuous and aligned glass-reinforced composite consists of
40 vol% of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened, display a modulus of 3.4 GPa.
Compute the modulus of elasticity of this composite in the longitudinal direction.
If the cross-sectional area is 250mm2 and a stress of 50 MPa is applied in this longitudinal direction, compute the magnitude of the load carries by each of the fiber and matrix phases.
Determine the strain that is sustained by each phase when the stress in part b is applied.
Compute the elastic modulus of the composite material, but assume that the stress is applied perpendicular to the direction of fiber alignment.
Assuming tensile strengths of 3.5 GPa and 69 MPa, respectively, for glass fibers and polyester resin, determine the longitudinal tensile strength of this fiber composite.

22. Equations on the calculation for long fiber reinforced matrix composite
longitudinal direction:
Transverse direction

23. Solution
We have
Ef = 69 GPa
Em = 3.4 GPa
Vf = 0.4
Vm = 0.6
The modulus of elasticity of the composite is calculated using equation

24. To solve this portion of the problem, first find the ration of fiber load to matrix load, using equation
or Ff =13.5Fm
In addition, the total force sustained by the composite Fc may be
computed from the applied stress s and total composites cross
section area Ac according to
However, this total load is just the sum of the loads carried by
fiber and matrix phases, that is Fc=Ff+Fm = N.
Substitution for Ff from the above yields
13.5Fm + Fm =12500N, Fm=862N
Whereas Ff=Fc- Fm=12500N-860N=11640N
Thus, the fiber phase supports the majority of the applied load.

25. The stress for both fiber and matrix phases must be calculated
The stress for both fiber and matrix phases must be calculated. Then, by using the elastic modulus for each (from part a), the strain values my determined.
For stress calculations, phase cross-sectional areas are necessary:
Am = VmAc= (0.6)(250mm2)=150mm2
and Af =VfAc = (0.4)(250mm2)=100mm2
Thus,
Finally, strains are commutated as
Therefore, strains for both matrix and fiber phases are identical,
which they should be, according to in the previous development.

26. d) According to equation
This value for Ect is slightly greater than that of the matrix phase, but, only approximately one-fifth of the modulus of elasticity along the fiber direction (Ecl), which indicates the degree of anisotropy of continuous and oriented fiber composites.
e) For the tensile strength TS,
(TS)cl = (TS)mVm +(TS)f Vf
(TS)cl=(69 MPa) (0.6) + (3.5 x 103MPa) (0.4)=1441 MPa