Composite Materials Research Progress

Damage Evaluation and Residual Strength Prediction of CFRP Laminates … 169
More details on AE methods can be found for example in [46].
Our contribution in this field is the introduction of a novel function able to combine the
acoustic energy released during an event and the strain energy stored in the material in that
moment. This function will be called “sentry” function because it signals important material
damage events during the tests, and its integral is related to the total damage and to the
residual strength as it will be shown in the next paragraph and in the examples.
The Sentry Function
In order to perform a deeper analysis of the laminate behaviour, a function that combines both
the mechanical and acoustic energy information [35, 47] is introduced. This function is
expressed in terms of the logarithm of the ratio between the strain energy (Es) and the
acoustic energy (Ea),
( )
( ) ⎟⎟
x ⎞
x
⎛ Es
f ( x)
= Ln ⎜
(1)
⎝ Ea
⎠
where x is the test driving variable (usually displacement or strain).
The function f(x) takes into account the continuous balancing between the stored strain
energy and the released acoustic energy due to damage. The function f(x) is generally
discontinuous and can be described by the combinations of four types of function, shown in
figure 2: (I) an increasing function PI(x), (II) a sudden drop function PII(x), (III) a constant
function PIII(x) and (IV) a decreasing function PIV(x).
These functions are defined over an “acoustic emission domain” (ΩAE) that correspond to
the displacement range over which the AE events were recorded. For all AE quantities ΩAE
represents the definition domain and outside the function of AE cumulative events,
cumulative counts, events energy and all other quantities related to the AE information are
null.
Dividing the AE domain ΩAE in sub-domain as reported in figure 2 it possible to write the
following relation:
Ω = Ω U Ω U Ω U Ω
(2)
AE AE,
I AE,
II AE,
III AE,
IV
In that condition the function f can be written as follow:
( x)
( x)
( x)
( x)
⎧ PI
⇔ x ∈ ΩAE,
I
⎪
⎪
PII
⇔ x ∈ ΩAE,
II
f = ⎨PIII
⇔ x ∈ ΩAE,
III
(3)
⎪PIV
⇔ x ∈ ΩAE,
IV
⎪
⎪⎩
0 x ∉Ω
AE