Composite Materials Research Progress

Damage Variables in Impact Testing of Composite Laminates 239
E
propagation
DuI = (1)
E
initiation
where Einitiation and Epropagation correspond to the energies absorbed before and after Fpeak,
respectively.
The ductility index is small for brittle materials, where most of the energy is absorbed
before Fpeak, and high for ductile materials, where most of the energy is absorbed after Fpeak is
exceeded. The energy absorption mechanisms before Fpeak are crazing and microcracking of
the matrix; whereas, after Fpeak, crack growth is observed via fiber pull-out, fiber/matrix
debonding and fiber fracture [26-29].
Other energy variables have been introduced since the DuI to rank impact performance.
In [12-13] Belingardi and Vadori introduced the Damage Degree (DD) defined as the ratio
between the absorbed energy (Ea) and the impact energy (Ei). Ei is the kinetic energy of the
impactor right before contact takes place and it is indeed the energy introduced into the
specimen. Ea can be calculated from the force-displacement curve as the area surrounded by
the curve in case of closed force-displacement curves (impact event with rebound) or the area
bounded by the force-displacement curve up to a constant level of force and the horizontal
axis in case of open force-displacement curves (impact event with no rebound). Based on the
energy viewpoint, penetration should take place the first time Ea reaches Ei. Therefore the DD
is below one for impact events with rebound while it reaches the value of one in case the
impactor is stopped with no rebound or specimen penetration is achieved. In [13-14], it was
shown that the relationship between the DD and the impact energy increases monotonically
until saturation and a fairly good data interpolation was achieved by a linear regression curve
[14]. A saturation energy level (Esa) was defined as the impact energy at which the DD
regression curve reaches the value of one. This energy threshold is of practical and theoretical
interest since it defines the maximum energy level the laminate can dissipate with no
penetration and by means of internal damage mechanisms only [12]. In synthesis, the DD is
defined as:
In [17,18], Liu proposed a second-order polynomial regression curve to describe the
absorbed energy vs. impact energy curve up to penetration (named by Liu the energy profile):
2
Ea = aEi
+ bEi
+ c
Depending on the laminate under study, the linear term and the constant c can be smaller
than the quadratic term so that equation (2) can be simplified as:
a
2
i
(2)
E ≅ aE
(3)
From the energy profile, Liu was able to define a Penetration Threshold (Pn) (in a series
of “continuous” impacts at increasing impact energies, it represents the first condition of no
impactor rebound and therefore of equality between impact and absorbed energy), and a
Perforation Threshold (Pr) (first condition of laminate complete perforation). Between the
penetration and perforation thresholds, there exists a range, named by Liu “the range of the
penetration process”, in which the impact energy and the absorbed energy are equal to each