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 Beznea

2

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.

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ISSN 0976 – 6340 (Print)

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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=TxR GPa;03.0=

TyR GPa;61.0=

CxR 2GPa;1.0=

CyR GPa07.0=xyR



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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 0

0 1 layer

2 layers

3 layers

4 layers

5 layers

2 biaxial 0,31 45

0 9 layers

3 uniaxial 0,62 900

8 layers

4 biaxial 0,31 45

0 7 layers

5 uniaxial 0,62 0

0 6 layers

6 uniaxial 0,62 0

0 5 layers

7 biaxial 0,31 45

0

8 uniaxial 0,62 900

9 biaxial 0,31 45

0

10 uniaxial 0,62 0

0

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.



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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.



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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 eT

tpptp

−

−+= 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.



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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.



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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

0.0

06

1

0.0

12

2

0.0

18

2

0.0

24

3

0.0

30

4

0.0

36

5

0.0

42

6

0.0

48

6

0.0

54

7

0.0

60

8

0.0

66

9

0.0

73

0

0.0

79

0

0.0

85

1

0.0

91

2

0.0

97

3

0.1

03

4

0.1

09

4

p [

Pa]

t [s]

p1 p2 p3 p4 p5 p6 p7 p8 p9 p10



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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

σσ σσeq

[M

Pa

]

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

σσ σσeq

[M

Pa

]

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

σσ σσeq

[M

Pa

]

Equivalent TNT mass

0.01 0.02 0.04 0.06 0.08 0.1



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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).

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