Composite Materials Research Progress

34
Jacquemin Frédéric and Fréour Sylvain
i*
For closed envelopes, the condition − 1 ≤ Fmmnn
≤ 1 has to be satisfied. But a more
detailed theoretical study (see Liu and Tsai, 1998) reduces the admissible range to the domain
1
[-1,0]. The same reference (Liu and Tsai, 1998) advises the choice of F -
2
* I
mmnn = for the
macroscopic interaction term (which corresponds to the generalised Von Mises model), since
this value is reasonable for a wide range of laminates. Taking into account this additional
I I
F = F ensures the
assumption in equation (56), the knowledge of I
F 1111 and
I
determination of the last two missing interaction terms 1122
F and
2222 3333
I
F 2233 , in stress space.
One similar method could be applied in order to determine the macroscopic strength
parameters expressed in strain space from the ultimate strains. Nevertheless, this method is
not useful in practice since uniaxial strains are difficult to apply to a sample. Thus, the
ultimate strains are generally deduced from the ultimate stresses: to reach this goal, one has to
introduce the macroscopic properties, i.e. the stiffness tensor L I , in order to relate both failure
criteria through Hooke’s law (33) expressed at macroscopic scale assuming a purely elastic
load.
5.2.3. Identification of the Microscopic Strength Parameter (of the Matrix Only)
Using an Inverse Method
From the standpoint of the structural designer, it is desirable to have failure criteria which are
applicable at the level of the lamina, the laminate, and the structural component.
Nevertheless, failure at macroscopic scale is often the consequence of an accumulation of
micro-level failure events (Tsai, 1987; Liu and Tsai, 1998). Laminated materials typically
exhibit many local failures prior to rupture. Thus, it is important to build up tools enabling to
enhance the understanding of micro-level failure mechanisms in order to develop higherstrength
materials. The ultimate goal is to have a failure theory that the designer can use with
confidence under the most general structural configuration and loading conditions and that the
developer of materials can use to design and fabricate new products to meet specific needs. In
order to reach this goal, the estimation of microscopic strength criteria would be of a valuable
help.
Since the epoxy resins involved in composite structures generally exhibit an isotropic
hygro-mechanical behaviour, the microscopic strength criterion expressed in terms of stresses
(54) simplifies as follows:
⎧
⎪1
⎨
⎪
⎩
= F
m
1111
+ F
m
11
⎛
⎜σ
⎝
m
2
11
+ σ
+ σ
m m m
( σ + σ + σ )
11
22
m
2
22
33
m
2
33
⎞
⎟ + 2F
⎠
m
1212
σ
m
2
12
+ 2 F
m
1122
m m m m m
[ σ ( σ + σ ) + σ σ ]
Thus, only four strength parameters have to be determined in order to enable failure
m m m m
predictions at microscopic scale:
F1111
, F1212
, F1122
, F11
.
Hypotheses being compatible
with the experimental observations are necessary to build an inverse model enabling the
11
22
33
22
33
(57)