World Journal Of Engineering
Numerical study of scale effects on the delamination of
laminates under low-velocity impact
Yajun Chen, Zhefeng Yu and Hai Wang
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, China.
the time must also be scaled as  ,besides, the
maximum strain in the plates is constant with
scaling if the impact velocity V is unchanged.
Introduction
Composite materials are widely used in
aerospace structures and automobile, since
they have a high specific strength and stiffness,
however, they are very susceptible to impact
loading, especially low-velocity impact.
Low-velocity impact can create internal
damage that often cannot be detected by visual
inspection. This internal damage can cause
reductions in strength by propagating under
loading[1].
In order to save time and expense, much
testing of composite components has to be
carried out on small-scale models by using
scaling laws, either on full-scale prototypes.
The impact damage in small-scale modes and
full-scale prototypes are different, the
relationship between them should be
understood. Several researcher have studied
scale effects in composite[2-5].
This work shows scale effects on impact
damage in laminates with different scale factor
by FEM method. The objective of the present
work was twofold. Firstly, a fully 3-D
composite damage model and VUMAT
subroutine implemented into ABAQUS are
used to predict damage induced by
low-velocity impact, especially delamination.
Secondly, the delamination size in models with
different scale factor is compared. The
relationship between delamination size and
size of model is studied.
Also the contact force scales as  2 , and if the
contact area scales geometrically the contact
pressure is unchanged. If the impactor also
scales geometrically, the impactor mass scales
as  3 . Further, the strain should increase
linearly with impact velocity. The present
results agree with these scaling rules.
Finite Element Model
Three plates of different geometrically
scaled are used to study scale effects on impact
damage. The plates made of T300/976 [7]
range in size from 30mm by 30mm by 2.3mm
thick to 120mm by 120mm by 9.2mm thick.
The material properties of T300/976
composites used in the calculations are listed
in Table 1. If the scale parameter is termed  ,
the dimensions of the plate are thus scaled
by   1, 2, 4 .The layup is (45)4 / (45)4 S .
The spherical impactors range in size from
16mm to 64mm.The mass of impactors varies
from 0.16kg to 10.24kg, with the mass varying
as the cube of the scale factor. The geometries
of plates and impactors are given in Table 2.
The plate specimens are clamped on four
edges.
Table 1 Material properties of T300/976
Elastic properties
Strength values
E11
156GPa
XT
1520MPa
Scaling Rules
E22= E33
9.09GPa
XC
1590MPa
The scaling rules are based on the dynamic
theorem and was particularly developed by
Qian and Swanson [6] for plates. They believe
that if the geometry of plates is scaled as  ，
G12= G13
6.96GPa
YT
45MPa
G23
3.24GPa
YC
252MPa
 12   13
0.228
S
105MPa
0.400

1540kg/m3
 23
199
World Journal Of Engineering
Table 2 Parameters of plates and impactors
Plate
Scale
size(mm)
thickness(mm)
Factor 
Cases
1
30 by 30
2.3
1
2
60 by 60
4.6
3
120 by 120
9.2
Cases
Plate
Table 3 Delamination area and length
Impactor
Cases
Diameter
(mm)
Impactor mass
(mm)
ratio
Area
Ratio
Scale
(mm)
L
(mm2)
A
Factor 
1
18.4
1
92
1
1
2
2
40.3
2.19
743
8.1
2
4
3
85.7
4.66
3941
42.8
4
As shown in Table 3, when scale factor is 2,
the delamination length along diagonal
direction scales 2.19. Hence, case 1 and case 2
have nearly same relative delamination size if
impact velocity varies inversely with square
root of plate length, this is confirmed by Y.
Qian[5] through experiments. If scale factor is
4, the delamination length along diagonal
direction scales 4.66, this is not very accord
with the conclusion put forward by Y. Qian.
Maybe other factors cause the discrepancy.
Moreover, in case 1, delamination occurs on
the interface near the back face, however, in
case 2 and case 3, delamination takes place on
the interface near the front face. The thickness
of plate effects the position where
delamination arises. The difference should be
studied in further work.
impact
velocity(m/s)
1
30 by 30
2.3
5.89
2
60 by 60
4.6
4.16
3
120 by 120
9.2
2.945
Length
A fully 3-D finite element model and Vumat
subroutine are used to predict damage in plates
under low-velocity impact. Intralaminar
damage is predicted through Modified
Chang-Chang criteria[8]. The delamination
between the ply interfaces is simulated by
interface elements. The laminate is modelled
with one element per ply. Zero thickness
cohesive elements are created between plies
with different angles.
Results and Conclusion
The results of simulation are presented as
follows. Figure 1 shows comparison of
delamination induced by impact in three
different size plates.
References
[1] Abrate S. Impact on composite structures.
Cambridge (UK):Cambridge University Press; 1998.
[2] Philippe Viot. Scale effects on the response of
composite
structures
under
impact
loading.
Engineering Fracture Mechanics 2008;75:2725-2736.
[3] Y. Qian. An Experimental Study of Scaling Rules
for Impact Damage in Fiber Composites. Journal of
Composite Materials 1990;24:559-570.
(a) case1 30mm by 30mm plate,
5.89m/s impact velocity
[4] Y. Qian. "Experimental Measurement of Impact
Response in Carbon/Epoxy Plates," Proc. AIAA,
ASME, ASCE, AHS, ASC 30th Structures, Structural
Dynamics, and Materials Conf., pp. 1023-1031 (1989).
[5] Chang, F. K. and L. B. Lessard. 1991. "Damage
(b)case2 60mm by 60mm plate,(c)case3 120mm by 120mm plate,
4.16m/s impact velocity
2.945m/s impact velocity
Tolerance of Laminated Composites Containing an
Open Hole and Subjected to Compressive Loading:
Fig 1. comparison of delamination in three
different size plates
The delamination area and delamination
length in diagonal direction are given in Table
3.
Part I-Analysis," J. of Composite Materials, 25:2-43.
[6] J.P. Hou. Prediction of impact damage in composite
plates. Composites Science and Technology 2000;
6060:273-281.
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