Composite Materials Research Progress

172
Giangiacomo Minak and Andrea Zucchelli
During the first phase, PI,1, the material is storing the strain energy, but when an internal
limit is reached a failure happens and the function f presents a first sudden drop (PII,1). After
this first drop the material starts again to store strain energy and it is interesting to notice that
the slope S1- of PI,1, before the event, is equal to the initial lope of PI,2 (S1+). The failure that
caused the first fall in this case does not affect significantly the material integrity (i.e. PII,1 is
not related to an important material modification). So the value of f(x) is reduced due to the
internal energy release, but the material strain energy capability is not compromised.
Different is the case represented by the second fall PII,2 in which the slope before (S2-)
and after (S2+) are different. This means that after PII,2 the material strain energy storing
capability is changed and because of an important material modification. In particular it is
interesting to notice that S2->S2+. After this event it is also reasonable to hypothesize that the
material damage increases. It was also previously observed [47], that typically after one or
two drops of f(x) characterized by the slope variation of PI(x) (S->S+) the next drop is
followed by a function of type III or IV. In figure 3B and figure 3C are reported two possible
situations that happen when the material damage has reached an important level. In the case
reported in figure 3B at the end of the storing energy phase PI,4 there is an instantaneous strain
energy release that causes the falling phase PII,3. The following constant behaviour of f(x),
described by PIII,1, is due to a progressive strain energy storing phase that is superimposed to
an equivalent material damage progression. The next fall PII,4 is followed by a decreasing
function PIV,1. The decreasing function type PIV, is related to the fact that the AE activity is
greater then the material strain energy storing capability: the damage has reached a maximum
and the material has no resources to bear the load. Then the phase PIV,1 in figure 3B indicates
that the material is totally damaged. In figure 3B between PIII,1 and PIV,1 there is a drop
function PII,4 that is due to an important failure inside the material, but this situation is not the
general one. In fact, sometimes it happens that after a constant trend of f(x) there are no more
drops and f(x) gradually decreases. This behaviour is due to a gradual damage progression
inside the material and no important failure events happen. At the opposite, the case
represented in figure 3C is related to a critical event inside the material: the strain energy
storing phase PI,5 is followed by a sudden drop PII,5 and then it follows a decreasing phase
PIV,2. This situation generally happens at the end of a test or, if it happens at the beginning it
reveals the presence of some defects inside the material.
The described analysis shows that the function f(x) can be usefully implemented to
describe the material damage progression because it takes into account both mechanical and
acoustic information. Summarizing we have that the increasing part of f(x) reveals the
material strain energy storing capability, the falls reveal the instantaneous release of the
stored energy due to failures, the constant and decreasing trends of f(x) prelude and describe
an important failure of the material structure. In the following sections two examples
regarding the application of different strategies about the use of the function f(x) to describe
the composite material damage are developed. In the first example the function f(x) is used to
determine the damage progression of five different types of laminates under in plane tensile
loading. In particular considering the function f(x) it was possible to identify the most
important material failure highlighted by the sub function PII,i. Then considering the stressstrain
information limited in the sub-domain ΩAE,I, ΩAE,III and ΩAE,IV, it was determined the
progressive stiffness reduction of the material.
In the first example the local structure of the function f(x) is used to interpret the stressstrain
data in order to determine the material damage model. While in the second example