Composite Materials Research Progress

Damage Evaluation and Residual Strength Prediction of CFRP Laminates … 201
3.3. Residual Tensile Strength
From the experimental results it was verified that the RTS of the laminates with [0,90,+45,-
45]s lay-up was greater than the [90,0,+45,-45]s one for each damage level. In [30] this result
is put into relation with the greater tensile fibre damage of the ply adjacent to the most
external one on the back side.
In figure 30 the tensile tests results are summarized in terms of RTS and the
correspondent values of the displacement.
RTS tests showed a reduction respect to undamaged specimens [35] even for the barely
visible indentations corresponding with Low damage levels. This is explained by the shear
fibre breakage shown in figure 24. This fibre failure mode, different from the tensile one, is
characterized by low strain energy level and, consequently, low acoustic energy emission.
Nevertheless the study of the function f can be useful to identify this kind of failure and an
example of this analysis was previously cited and it is reported in figure 29 B. In particular
from the diagram in figure 29B the important drop of f at a displacement of 3.5 takes into
account a low value of strain energy stored in the laminate (Es = 1.3 J) and an AE event with
low energy content (Ea = 3.810-6 J). In order to take into account the material damage it is
necessary to evaluate all events that cause loss of structural integrity. Since the function f
amplifies the most important material damage events and it is able consider at the same time
the strain energy storing capability and the released internal energy, its integral was utilized
as a damage indicator. In figure 31 the RTS data are plotted versus the respective values of
Int(f) for each laminate type. In particular it is evident the negative relation between the RTS
and the values of the f integrate, confirming, as presented by other authors using different
damage indicators [49-52], that the variable Int(f) is a reliable instrument to evaluate the
material damage during the indentation process.
To represent mathematically the relations between RTS and the damage indicator many
different approaches are utilized: discontinuous relations are composed by linear[49] or non
linear [50] equations and they present a threshold at the damage indicator, so values of
damage indicator lower to a specified threshold value do not change the RTS that is so equal
to the virgin material tensile strength; on the contrary continuous relations[51, 52] have a
plateau which value is equal to the virgin material tensile strength when the damage indicator
in zero and they have a curvature inversion.
In the present work in order to relate the Int(f) and the RTS a continuous relation was
considered having the following form:
C
BInt ( ( f)
)
RTS Ae −
= (2)
Where the constant A is related to the ultimate load of the virgin material, and the
constant B and C can be obtained by means of a linear regression based on the experimental
data. Implementing the model in (2) to the experimental data it was estimated the following
values for the coefficient of the continuous model:
- A = 39 kN
- laminate configuration [0,90,+45,-45]s: B = 8.8 10 -5 ; C = 2.0 (mm -1 );
- laminate configuration [90,0,+45,-45]s: B = 8.3 10 -7 ; C = 2.8 (mm -1 );