Experimental Model of The Semicircular Laminated Composite Curved Bars

7/31/2019 Experimental Model of The Semicircular Laminated Composite Curved Bars

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(Manuscript No: I12528-11)

April 19, 2012/Accepted: April 25, 2012

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Experimental Model of The Semicircular

Laminated Composite Curved Bars

Serhii Meckaelovech Vereshaka

Sumy State University

Sumy, Ukraine.

Tel: +380 542 334058, Fax: +380 542 334058

(Email: [email protected])

Emad Toma Karash

Sumy State University

Sumy, Ukraine.

Tel: +380 542 334058, Fax: +380 542 334058

(Email: [email protected])

Abstract - The classical anisotropic elasticity theory was used to construct multilayer theory for the calculation

of the stress and deformation fields induced in the multilayered composite semicircular curved bar subjected to

end forces. The radial location and intensity of the open mode radial stresses, tangential stresses were calculatedand compared with the results obtained from the experiments results, anisotropic continuum theory and ANSYS

method. The multilayer theory gave more accurate prediction of the location and intensity of the open moderadial stresses, tangential stresses and displacements than those calculated from the anisotropic continuum

theory. The experimental results were identical to the results of multilayer theory.

Keywords: Multilayer theory, Delamination, Anisotropic continuum theory, ANSYS method .

Introduction

Lightweight structures that meet even exceed the performance and safety requirements in the strictest sense aregaining more importance. Fibres reinforced polymer composites have been shown to perform successfully in

many structural applications, and it is expected their use will increase further in the upcoming years. Applicationof composite materials can be found from aerospace, marine, automotive areas to biomedical implants.

Composite materials fall into the general category of anisotropic materials, for which the material properties

exhibit directional characteristics. On the other hand the most common engineering materials such as steel etc.,

are considered isotropic for which there is no dependence of material properties on direction. Isotropic materials

can be characterized by two independent material constants only, but for anisotropic materials the number of

constants can be as high as 21depending on the number of planes of material symmetry the material possesses[1-6]. In most engineering applications, laminated composite structures have certain curvatures (for example,

curved panels and curved beams). If the curved composite structure is .subjected to bending that tends to flatten

the composite structure, tensile stresses can be generated in the thickness direction of the com-posites. Also,shear stresses could be induced if the bending is not a "pure" bending. Under normal operations, if the above

type of bending occurs cyclically, open-mode delaminations or shear-mode delaminations could nucleate at the

sites of peak interlaminar tensile stresses or at the sites of peak interlaminar shear stresses. Continuation of these

bending cycling will cause the delamination zones to grow in size and ultimately cause the composite

structures to lose their structural integrity (loss of stiffness and strength) due to excessive delaminations. Thetype of delamination failure (open mode or shear mode) depends on which type of interlaminar strength (tensile

or shear) is reached first [7-10]. The MATH-CAT 14 method were used to perform similar delaminationanalysis of the multilayered semicircular composite curved bar subjected to end forces and end moments. The

resulting predictions of locations and intensities of peak radial stresses are compared with the results of theanisotropic continuum theory presented in reference [9].


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International Journal Of Structronics & Mechatronics

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Composite curved bar

In Fig. 1 shows the geometry of a composite curved bars thickness t, having cylindrical anisotropy. Curved

beams in terms limited to two concentric circles of radii ri and ro, as well as two radial planes which form an

angle = / 2. It is assumed that the material is orthotropic bar and a plane of elastic symmetry coincides withthe middle surface of the rod. Anisotropy axis is perpendicular to the planes of elastic symmetry through the

common center of concentric circles and coincides with the z axis of the cylindrical coordinate system. The axis

ofx, from which the measured polar angle , coincides with the y-axis of a Cartesian coordinate system. It is

believed that the curved side of r = riand r = ro is not loaded. At the ends of the hinged beam are oppositely

directed vertical forces P. Thus, using the principle of superposition of the given load (Fig. 2) can be representedas the sum of the concentrated force P and a concentrated bending moment M = F. d

Figure 1 : Laminated composite curved-bar coupon for study

Figure 2 : Bending of curved bar by forces at its ends

Anisotropic continuum theory

For bending a linearly elastic continuous curved bar with cylindrical anisotropy. The Airy stress function F.

written in cylindrical coordinate system takes on the following functional forms [5].

Multilayer theory

Figure 3 shows the multilayer (N-layers), semicircular curved bar subjected to both end forces and end moments

M. The stress field and displacement field in each layer i (i=1, 2 N) For each loading case may be obtained

from the results given in section 3.


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Serhii Meckaelovech Vereshaka, Emad Toma Karash

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Discrete structure theory of laminated beams with ideal contact layers

In Fig. 3 shows a multilayer flat bar bent in the shape of semicircles in the plan, each of the ends of which are

concentrated transverse force P and bending moment M. Model consists of N layers. Field of stresses and

displacements of each layer i (i = 1, 2... N)

Figure 3: Bending of laminated anisotropic semicircular curved bar by end forces

Discrete structure theory of laminated beams with non-ideal contact layers

Let a plane between the layers of curved rod (Fig. 3) for certain values of external load due to the destruction of

the adhesive layer [11] may cause an elastic slip two neighboring layers relative to each other. In this case the

difference between the displacement in the circumferential direction),a(u),,a(u i

)i(i

)i(

1

the mating

surfaces of adjacent layers and shear stresses),a( i

)i(r , when i

ar(. 3), there is a relationship.

1. )((i))1()( K),(),( iri

i

i

iauau

In general, the parameter ),a(KK i(i)(i) . As the limit of equation (37) we have two options: the 01

(i)/K

- There is a perfect slip at 0(i)

K perfect contact. Assuming that the radial stresses),a( i

)i(r

),a(u i)i(

r when passing through the surface of the layer jump are not static and kinematic conditions of non-ideal contact

for the given external loads.

Finite element approach

By using Ansys 10.0 finite element analysis software, a static failure analysis was performed on an element of a

composite curved bar. First element type was defined with solid layered 46 Figure 4. Solid46 is a layeredversion of the 8-node structural solid element designed to model layered thick shells or solids. The element

allows up to 250 different material layers. The element may also be stacked as an alternative approach. Theelement has three degrees of freedom at each node: translations in the nodal x, y, and z directions.


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Figure 4: SOLID46 Geometr

Real constant sets were defined for 54 layers, various orientation angle and each layers thickness was entered0.37 mm. After material properties was defined, linear orthotropic material was chosen and the mechanical

properties of graphite-epoxy composite material was added as EX, EY, EZ, PRXY, PRYZ, PRXZ, GXY, GYZ

and GXZ. In order to calculate failure criteria, ultimate tensile strength, compressive strength and shear strength

were entered both in fiber direction and in matrix direction. Then a volume block was modeled and material

properties, real constant sets and element type were appointed to this volume. After that the model was meshedby using hexahedral sweeped elements.

Figure 5- Shows the model design and results deformed shape model under end force F

Results and Dissection

A. NUMERICAL SOLUTIONSAs an example, the calculation considered the stress-strain state of flat curved bars in bending. Bruce takes theform of semicircles in plan and is made of laminated glass with 16 layers of unidirectional stacking with the

specified scheme. Geometrical parameters of a rod (Fig. 1): cross-sectional dimensions - h = 48 mm, t = 4 mm,

the radii of the inner and outer surfaces of the timber - a = 96 mm, b = 100 mm, the radius of the middle surfaceof am = (a + b) / 2 = 98 mm.


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The elastic characteristics were determined by the glass method proposed in [12]. The elastic moduli, shearmodulus and Poisson's ratio wound tapes, recruited from the alumina borosilicate fibers, respectively. As the

matrix glass epoxy resin with the following parameters of elasticity: Each monolayer thickness of 0.25 mm

volume occupied by the ribbons, about 70% of the total.

Technical constant of laminated glass under consideration for different schemes of reinforcement aresummarized in Table 1.

reinforcement

schemePE, PG, ij ji k

]0/75/0

/75/75/

0/75/0[

42

24

22280

36300

25920

r

z

E

E

E

6624

5014

7493z

r

zr

G

G

G

397.0

397.0

234.0z

r

rz

265.0

311.0

221.0z

r

zr

1.276 2.705

]0/75/75/0[ 22

22380

33280

28380

r

z

E

E

E

6203

5438

7747z

r

zr

G

G

G

394.0

395.0

188.0z

r

rz

265.0

311.0

221.0

zr

z

r

1.219 2.658

]0/75/75/0[ 22

22350

34630

2732

r

z

E

E

E

6391

5250

7642z

r

zr

G

G

G

396.0

396.0

178.0z

r

rz

255.0

324.0

226.0

zr

z

r

1.245 2.679

Table 1 the elastic characteristics of the GRP.

We consider three computational models of the rod. The first model is a timber as an anisotropic continuum

]0/75/0/75/75/0/75/0[ 4224

with the following physic-mechanical characteristics (Table1):

PE 36300 , P 22280r

, PGr 6620

, 396.0r

, 705.2 , 276.1k .

The following boundary conditions. It is believed that at the end of the rod, at = 0, the displacement in the

circumferential direction are zero, i.e.0)0,( ru

P

,0)0,( ru

M

. In addition, based on the symmetry conditions

of shear strain, a cross-section of the rod with coordinate = / 2 will be equal to zero, i.e.0)2/,( r

P

r ,

0)2/,( rM

r .

Discrete structure theory with a perfect contact of adjacent layers of lumber used in the calculation of the secondmodel. It was believed that the beam consists of three layers of unidirectional (N = 3). The first (i = 1) and third

(i = 3) layers of code]75/75/0[ 3

]0/75[ 4

have the following options

MPaEE 37300)3()1(

,P22300EE

3

rr

,PGG 6760

)3(

r

)1(

r ,397.0

)3()1(

r r

,

658.2)3()1(

, 219.1kk)3()1( ; the second layer (i = 2) with the code

]0/75/75/0[ 22

respectively PE P E 22320,34600

)2(

r

)2(

,PG 6380

)2(

r ,394.0

)2(

r

,679.2

)2( ,

245.1k)2( . For the continuous the third model beam, which corresponds to a discrete structure theory

with imperfect contact of adjacent layers, identical to the second model. The main difference between these twomodels - different contact conditions on the mating surfaces of adjacent layers. In Fig. 4 shows graphs of normal

tangential stresses P beam thickness, depending on the conditions of contact on the mating surfaces ofadjacent layers. Graphs of displacement in the radial direction along the outer face of the timber. The results

presented here were obtained by the action of concentrated tensile force P = 180 N (Fig. 2b) is applied without

eccentricity. For a comparative analysis considered three simulation models of the rod. Graphs of stresses and

displacements obtained under continuous structural theory are given by dash dotted lines. The solid lines showthe results that correspond to discrete structural theory of multilayer timber according to both ideal and non-

ideal contact associated facial surfaces of adjacent layers. The values of coefficients K i (i=1, 2) for the


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considered three-layer beam (1) are identical, i.e. for the considered three-layer beam (1) are identical, i.e. K1 =K2 = K.

B. EXPERIMENT DETAILSFilament wound composite materials are used in commercial industries such as fuel tank, portable oxygen

storage, and natural gas .The fibers used were semicircular bars. The bars typically 192 mm inner diameter , 200

mm outer diameter, 4 mm thickness, 48 mm width . WE linked twelve Strain gauges on the model from insideand outside shown in Figure 6 (a, b, c).

Figure 6: Shown the bars, strain gauges and instruments were used in experiment

Table 2 summarizes all the values of (r, , Ur, U) calculated from different theories and experimental results.

UUroutmediuminroutrmediumrinTheory

7.628.37-142.20139.801.390Anisotropic continuum5.977.25-12713.8147.701.40SYANA1.531.39-109.411.49801.360

Multilayer theory

ideal contact8.38.17-201.723.418401.490

Multilayer theory

Non- ideal contact

76457.64.- 4714.557.5Experiment results

Table 2 Intensities and locations of delamination stresses in semicircular curved bar end force


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Conclusion

In summary, compare between experimental results and based on the classical theory of elasticity of anisotropic

bodies and discrete structure theory of multilayer investigation of the stress strain state of the flat curved bars,

allows the following conclusions. Model of laminated timber, where the elastic slip allowed the mating surfacesof adjacent layers relative to each other, partly reflects the real picture of the deformation of such a structural

element. Compare the results extracted from the various theories with the experimental work, it is clear that theresults were in the match is acceptable with the experimental work, as well as that the results derived from the

theory of multi layers to be more robust in terms of design to radial stresses and tangential stresses, as well as be

more resistant to the horizontal and vertical displacements.

References

1. Whetstone, W. D., SPAR Structural Analysis System Reference Manual, System Level 13A, Vol. 1,Program Execution, NASA CR-158970-1, Dec. 1978.

2. Ko, William L., Delamination Stresses in Semicircular Laminated Composite Bars, NASA TM-4026, Jan.1988.

3. Ko, William L. and Raymond H. Jackson, Multilayer Theory for Delamination Analysis of a CompositeCurved Bar Subjected to End Forces and End Moments, NASA TM-4139, Sept. 1989. Also published in

Composite Structures 5, I. H. Marshall, ed., Elsevier Applied Science, London, 1989, pp. 173198.

4. Ko, William L. and Raymond H. Jackson, Open-Mode Delamination Stress Concentrations in Horseshoeand Elliptic Composite Curved Bars Subjected to End Forces, NASA TM-4164, Jan. 1990.

5. Lekhnitskii, S. G., Anisotropic Plates, Gordon and Breach Science Publishers, New York, 1968.6. Fung, Y. C., Foundations solid Mechanics, Prentice-Hall, Inc . Englewood Cliffs, New Jersey, 19657. Whetstone, W.O., SPAR Structural Analysis System Reference Manual, System Level 13A, Vol. I,

Program Execution, NASA CR-15897o-1, 1978.8. A. Puck. Festigkeitsanalyse von Faser-Matrix-Laminaten. Carl Hanser Verlag, Munchen Wien, Germany,

1996.9. C. Schuecker. Mechanism based modeling of damage and failure in fiber reinforced Polymer laminates.

PhD Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology,Vienna, Austria, 2005 thesis.

10. C. Schuecker, D.H. Pahr, and H.E. Pettermann. Accounting for residual stresses in FEM analyses oflaminated structures using the Puck criterion for three-axial stress states. Comp. Sci. and Tech.

66(13):20542062, 2006.

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Experimental Model of The Semicircular Laminated Composite Curved Bars