Investigation into the effects of delamination parameters of the layered compo

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
338
INVESTIGATION INTO THE EFFECTS OF DELAMINATION
PARAMETERS OF THE LAYERED COMPOSITE PLATES DURING CLOSE
PROXIMITY BLAST LOADS
Ionel Chirica1
, Elena Felicia Beznea2
1,2
Department of Applied Mechanics, “Dunarea de Jos” University of Galati,
47, Domneasca Str., Galati-800008, Romania
ABSTRACT
Results of the study concerning the protective capacity of delaminated layered composites
subjected to an explosion of a spherical charge are presented in this paper. Main objective of this
analysis is to investigate the effect of the central circular delamination parameters on the layered
composite plate behavior during the blast load in air. The explosion center is considered to be placed
in the close proximity of the plate. Various scenarios (parametric calculus) to evaluate the behavior
of the layered composite plate to blast loading are presented: position within the thickness,
delamination area per plate area ratio, charge weight. A nonlinear analysis with the finite-element
computer code COSMOS/M was done. The methodology for the blast pressure charging and the
mechanism of the blast wave in free air for a layered plate belonging to a ship hull structure are
given. The spatial pressure variation is determined by using Friedlander exponential decay equation.
The delamination model using finite elements and interfacial constrain conditions are presented. The
numerical results show that delamination presence within the layered composite decreases the
protective capacity of the structure to explosion charge. The graphical results are presented for
various positions of delamination, equivalent TNT mass and delamination area ratios.
Keywords: Blast loads, delaminated plates, FEM analysis, layered composites
1. INTRODUCTION
Laminated composite panels, which are anisotropic, are gaining popularity in structural
applications such as ship hulls, decks, ship and offshore superstructures. The use of laminated
composites provides flexibility to tailor different properties of the structural elements to achieve the
stiffness and strength characteristics. However, these materials are prone to a wide range of defects
and damage that can cause significant reductions in stiffness and strength. Delamination is one of the
most common failure modes in composite materials which affect the overall stiffness of the structure.
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 4, July - August (2013), pp. 338-347
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2013): 5.7731 (Calculated by GISI)
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IJMET
© I A E M E

339
In the last decade, blast loads induced by explosions produced by accidents or intentionally
by terrorist attacks within or immediately nearby ship hull can cause catastrophic damage on the ship
structure, loss of life and injuries to crew and passengers [1]. To analyze and design a structure
subjected to blast loads a detailed understanding of blast phenomena and the dynamic response of
various structural elements are necessary. To diminish the injuries due to blast loading it is necessary
to do various scenarios to evaluating the behavior of the ship structure to blast loading (explosive
magnitude, distance from source of explosion, structure scantling, the structure imperfection etc.).
In close proximity to an explosion, the ship hull structures are loaded by a high intensity-
short duration pressures that vary in time and space.
Most part of the literature available concerning plate response to short-duration, high
intensity pressures make this assumption. Experimental evidence supporting this assumption is
provided in [2]. In many of these works, the time history of the spatially uniform pressure is
described by step-pulse, N-pulse, or Friedlander equations [3].
Finite element modeling and analysis for the blast-loaded structures are also presented in. The
particular equation used for the pressure-time history of the load is often chosen to best match the
particular phenomenon; considered. The time history of overpressures due to explosions is often
represented by the modified Friedlander exponential decay equation ([4]-[6]).
In the references listed thus far, the blast pressures are of arbitrary magnitude and are applied
uniformly across the structure. Methods presented in [7] use experimental data from explosive tests
to develop expressions for the blast overpressure as a function of time and distance from the blast, as
well as charge weight and other important blast parameters. Very few papers make use of such a
realistic blast load. Most of the literature available concerning impulsively loaded plates considers a
linear solution for isotropic plates. There are also many linear solutions available for impulsively
loaded composite plates, and some of the references listed thus far are of this type [8].
The rapid expansion of the detonation products creates a shock wave in the surrounding
medium, which for simplicity in this paper is assumed as being in air. This shock wave in air is
known as a blast wave. Similar to the detonation wave there is for practical purposes, a discontinuous
increase in pressure, density, temperature and velocity across a blast wave. The shock-induced
compression of the ambient air also leads to an increase in temperature behind the shock front. The
pre and post shock states are described by conservation equations for mass, momentum and energy,
collectively known as Rankine-Hugoniot Jump equations ([9]).
In [10] a reliability-based design approach is suggested where system reliability is used to
compute the probability of failure of a composite laminate. A case study for the design of a layered
composite laminate and subjected to uncertain blast event is demonstrated.
Estimating the structural response to such an explosion requires accurate prediction of the
applied pressures and a solution procedure that is adequate for such transient phenomena.
The work presented here focuses on the structural response to such close proximity
explosions of the delaminated layered composite plates having an imperfection, such as
delamination. The nonlinear solution is developed for these simulations.
2. CHARACTERISTICS OF THE LAYERED COMPOSITE PLATE
The geometry of the plate, belonging to a ship hull composite structure is a square plate
having the side of 320mm and total thickness t=4.96mm. The plate has 10 symmetrical layers, made
of e-glass epoxy, with the characteristics: Ex = 3.86GPa; Ey = 8.27GPa; Gxy = 4.14GPa; xyµ =0.26.
The tension (T) and compression (C) strengths of the material are:
GPa;06.1=T
xR GPa;03.0=T
yR GPa;61.0=C
xR 2GPa;1.0=C
yR GPa07.0=xyR

340
In the Table 1, the characteristics of each layer (thickness and fiber direction) are shown. As
it is seen, there are two types of layers: uniaxial layers with and biaxial layers.
In the Table 1 is presented also the position of delamination for each case.
Table 1 Layered composite characteristics
No.
Layer
type
t [mm] α
Position of delamination
Case a Case b Case c Case d Case e
1 uniaxial 0,62 00
1 layer
2 layers
3 layers
4 layers
5 layers
2 biaxial 0,31 450
9 layers
3 uniaxial 0,62 900
8 layers
4 biaxial 0,31 450
7 layers
5 uniaxial
0,62 00
6 layers
6 uniaxial
0,62 00
5 layers
7 biaxial
0,31 450
8 uniaxial 0,62 900
9 biaxial 0,31 450
10 uniaxial 0,62 00
3. DELAMINATION MODEL
The finite element delamination analysis was carried out using COSMOS/M finite element
software. For the present study, a 3-D model with 3-node SHELL3L composite element of
COSMOS/M is used. The panel is divided into two sub-laminates by a hypothetical plane containing
the delamination. For this reason, the present finite element model would be referred to as two sub-
laminate model. The two sub-laminates are modeled separately using 3-node SHELL3L composite
element, and then joined face to face with appropriate interfacial constraint conditions for the
corresponding nodes on the sub-laminates, depending on whether the nodes lie in the delaminated or
undelaminated region. The delamination model has been developed by using the surface-to-surface
contact option (Fig. 1). The contact algorithm of COSMOS/M determines which node of the so-
called master surface is in contact with a given node on the slave surface.
In the analysis, the certain layers are intentionally not connected to each other in delaminated region.
The hypothesis used in the nonlinear calculus is that the delaminated region does not grow. At the
boundary of the delamination zones the nodes of one row are connected to the corresponding nodes
of the regular region by master slave node system.

341
Figure 1: Delamination model
In the calculus done in this paper, the delamination has a circular shape, placed in the middle
of the plate, between two sequential layers (see Table 1).
4. THE MAIN CHARACTERISTICS OF THE BLAST WAVE
Blast resistant design of ship hull structure, made of layered compo-sites, generally provides
sufficient toughness of components and structural system capable of limiting the possibility of hull
collapse. Therefore, simula-tion of blast loading and estimation of structure behavior and damage
under blast loading are very important phase of research to evaluate the resistance and safety of ship
hull structure against direct and consequential blast damage.
In a blast analysis, one can find the size and location of the explosion to protect against. By
using the relationship that the intensity of a blast decays in relation to the cube of the distance from
the explosion one can adopt an idealized blast wave and at the target. The positive phase duration of
the blast wave is compared with the natural period of response of the structure.
The pressure at a specific point in air in the path of an explosion over time will follow the
same general pattern, so long as does not exist any reflection from nearby objects. This pattern,
called an overpressure curve (Fig. 2) has main components: the detonation, arrival time (ta), peak
pressure (ps), and time duration (Ts). The detonation can be considered as time 0, while the arrival
time is the time that it takes for the pressure wave to reach the point of interest. Once the peak
pressure is reached, it immediately starts to decay to the normal pressure during the time duration. As
the material in the blast wave expands outward it can leave a void, creating a region with pressure
lower than normal atmospheric pressure.

342
Figure 2: Typical blast pressure versus time profile
For describing the pressure-time history of a blast wave, certain equations have been
developed and used in the calculus. The most frequently used is the modified Friedlander equation,
describing the pressure after its arrival
sT
bt
s
s e
T
t
pptp
−






−+= 1)( 0 (1)
In equation (1), ps denotes the peak reflected pressure in excess of the ambient one; Ts
denotes the positive phase duration of the pulse measured from the time of impact of the structure
and b denotes a decay parameter which has to be adjusted to approximate the overpressure signature
from the blast tests.
Blast wave parameters for conventional high explosive materials have been the focus of a
number of studies during the 1950’s and 1960’s. Estimations of peak overpressure ps (in kPa) due to
spherical blast based on scaled distance Z, were introduced in [11] as:
- for ps > 1000kPa: 100/670 3
+= Zps ,
- for 10 < ps < 1000kPa: 9.1/585/5.145/5.97 32
−++= ZZZps ,
where Z is the dimensional distance parameter (scaled distance): Z = R/W1/3
.
R is the actual effective distance from the explosion and W (equivalent TNT mass, in kg).
Scaling laws provide parametric correlations between a particular explosion and a standard charge of
the same substance.
In Fig. 3, the methodology and model to determine the pressure from blast loading is
presented. According to the actual effective distance from the explosion R, elements within 45
degrees of the blast normal distance vector, h, are divided into groups based upon their average
distance to the center node.
Only elements within the 45 degree cone are loaded (circle with the radius RG). The area
within the cone is divided into a number of rings to determine the pressure acting on the elements of
the mesh. The distribution of the blast load on the plate using 10 load rings is shown in the Fig. 4.

343
The time duration Ts is determined from a natural vibration calculus, being equal to natural period of
response of the structure ([12]).
Center node 45o
Explosion point
R
Loaded surface
Blast normal distance vector
G
h
R
Circle of loaded elements
Figure 3: Blast pressure evaluation model
Figure 4: Distribution of the blast load on the plate using 10 load rings
5. FEM ANALYSIS OF THE DELAMINATED PLATE
The parametric studies were carried out on a square plate from the ship structure placed
between two pairs of web stiffeners. Therefore, the plate can be considered as being clamped on all
sides.
In the non-linear calculus, Tsai-Wu failure criterion was used for the limit state stresses
evaluation (equivalent stresses).
The FEM parametric calculus was done for various values for: equivalent TNT mass, W
(0.01kg, 0.015kg, 0.05kg, 0.1kg and 0.2kg), position of the delamination along the thickness (see
Table 1) and delamination area ratio (ratio k=delamination area/plate surface area, equal to 0.01,
0.02, 0.06, 0.08 and 0.1). The blast normal distance vector, h, is equal to 0.14m.

344
Figure 5: Pressure - time histories for all rings, for W=0.01kg
In the Fig. 5, the variation of the pressure (pi) on each ring i, for the period of 0.1s,
corresponding to an equivalent TNT mass, W=0.01kg, is shown.
Time variation of the maximum stress obtained in the point placed on the middle of the plate,
versus equivalent TNT mass, W, for the imposed values of the delamination ratio, k (0.01, 0.02, 0.04,
0.06, 0.08, 0.1), for the positions of the delamination shown in Table 1, have been determined.
In Figs. 6, 7 and 8 only the results obtained for the three cases are shown: case a
(delamination between layers 1 and 2), case c (delamination between layers 3 and 4) and case e
(delamination between layers 5 and 6). As it is seen in Figs. 6, 7, and 8, the ratio between the
maximum stress occurring in the case of W=0.1kg and the maximum stress occurring in the case of
W=0.01kg is about 2.5 for the case a, and about 1.5 for the case e. Also, the maximum value of the
equivalent stress in the case a, is about double versus the maximum value of the equivalent stress in
the case e, for the same amount of equivalent TNT mass (0.2kg). Observing the all three figures, an
important remark reveals that the case with the delamination position as closed as to the middle of
the plate thickness is a safety case.
0
500
1000
1500
2000
2500
3000
3500
0.0061
0.0122
0.0182
0.0243
0.0304
0.0365
0.0426
0.0486
0.0547
0.0608
0.0669
0.0730
0.0790
0.0851
0.0912
0.0973
0.1034
0.1094
p[Pa]
t [s]
p1 p2 p3 p4 p5 p6 p7 p8 p9 p10

345
Figure 6: Case a - Maximum stress versus equivalent TNT mass, W, for each delamination area
ratio, k
Figure 7: Case c - Maximum stress versus equivalent TNT mass, W, for each delamination area
ratio, k
Figure 8: Case e - Maximum stress versus equivalent TNT mass, W, for each delamination area
ratio, k
0
0.1
0.2
0.3
0.4
0.01 kg 0.015 kg 0.05 kg 0.1 kg 0.2 kg
σσσσeq[MPa]
Equivalent TNT mass
0.01 0.02 0.04 0.06 0.08 0.1
0
0.05
0.1
0.15
0.2
0.01 kg 0.015 kg 0.05 kg 0.1 kg 0.2 kg
σσσσeq[MPa]
Equivalent TNT mass
0.01 0.02 0.04 0.06 0.08 0.1
0
0.05
0.1
0.15
0.01 kg 0.015 kg 0.05 kg 0.1 kg 0.2 kg
σσσσeq[MPa]
Equivalent TNT mass
0.01 0.02 0.04 0.06 0.08 0.1

346
6. CONCLUSIONS
In this research paper, a FEM based methodology has been developed for the evaluation
of the effects of delamination parameters of the layered plates used in ship hull structure during
close proximity blast loads.
In the paper, a nonlinear dynamic calculus was done with COSMOS/M soft package
using specific elements adapted for composite layered structures.
For the values of the equivalent TNT mass W lesser than 0.1kg, the fails do not occur in
the material and so the integrity of the plate is not affected. In the case of W equal to 0.2kg, in all
cases of area ratios k and position of delamination, the tension fails occurs (named Fail 1,
according to Tsai-Wu failure criterion). The variations of stress determined with Tsai-Wu failure
criterion are presented in Figs. 6, 7 and 8 for three cases of position of delamination.
As it is seen in the figures with the results, the stresses are decreasing since the position of
the central delamination is more closed to the middle of the plate thickness. Also the stresses are
increasing since the delamination area is increasing. Therefore, in the evaluation of structure
performance in the case of a delamination is occurring due to various reasons, the upper
conclusions are very important.
In the shipbuilding it is recommended that guidelines on abnormal load cases and
provisions on progressive collapse prevention should be included in the current ship hull
structure design norms (especially in the case of using the composite layered material).
Requirements on ductility levels also help improve the structure performance under severe load
conditions (bomb blast, high velocity impact etc.).
ACKNOWLEDGEMENT
The work has been performed in the scope of the Romanian Project PN2, Code 162EU
(2011-2014).
REFERENCES
[1] W. Baker, Explosions in air, (University of Texas Press, Austin, 1973).
[2] L. Librescu and A. Nosier, Response of Shear Deformable Elastic Laminated Composite
Flat Panels to Sonic Boom and Explosive Blast Loadings, AIAA Journal, 23(2), 1990,
345-352.
[3] M.L. Crocker and R.R. Hudson, Structural Response to Sonic Booms, J. of Sound and
Vibration, 9(3), 1969, 454-468.
[4] H. S. Türkmen, Structural Response of Laminated Composite Shells Subjected to Blast
Loading: Comparison of Experimental and Theoretical Methods, Journal of Sound and
Vibration, 249-4(24), 2002, 663-678.
[5] I. Chirica, D. Boazu and E.F. Beznea, Response of Ship Hull Laminated Plates to Close
Proximity Blast Loads, Computational Material Science 52(4), 2012, 197-203.
[6] A. Kadid, Stiffened Plates Subjected to Uniform Blast Loading, Journal of Civil
Engineering and Management, 14(3), 2008, 155-161.
[7] FEMA 426, Reference manual to mitigate potential terrorist attacks against buildings.
Providing protection to people and buildings (Risk Management Series. New York,
2003).
[8] P. Cooper, Explosive engineering (Wiley-VCH, New York, 1996).

347
[9] G. Kinney and K. Graham, Explosive shocks in air (2-nd Ed., Springer Verlag, New
York, 1985).
[10] A.B. Altunc, J.J. Kim, M. Al-Haik and M.M. Reda Taha, Reliability-based design of
blast-resistant composite laminates incorporating carbon nanotubes, Composite
Structures, v. 93 (8), 2011, 2042-2048.
[11] H.L. Brode, Numerical solution of spherical blast waves, Journal of Applied Physics,
American Institute of Physics, New York, 1955, 21-46.
[12] J. Son, Performance of cable supported bridge decks subjected to blast loads, University
of California, Berkeley, 2008.
[13] Prof.M.R.Wakchaure and S.T.Borole, “Comparison of the Lateral Deflection at Midpoint
of Long & Short Side Column Under Blast Loading”, International Journal of Civil
Engineering & Technology (IJCIET), Volume 4, Issue 4, 2013, pp. 106 - 112, ISSN Print:
0976 – 6308, ISSN Online: 0976 – 6316.
[14] Mohammed S. Al-Ansari, “Building Response to Blast and Earthquake Loading”,
International Journal of Civil Engineering & Technology (IJCIET), Volume 3, Issue 2,
2012, pp. 327 - 346, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.

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