factors affecting critical buckling load of reinforced...

International Journal of Current Engineering and Technology E-ISSN 2277 – 4106, P-ISSN 2347 – 5161 ©2017 INPRESSCO®, All Rights Reserved Available at http://inpressco.com/category/ijcet

Research Article

1531| International Journal of Current Engineering and Technology, Vol.7, No.4 (Aug 2017)

Factors affecting critical buckling load of reinforced beam

Ali adel battawi*

The Technical College, The Middle Technical University, Baghdad, Iraq. Received 30 May 2017, Accepted 31 July 2017, Available online 10 Aug 2017, Vol.7, No.4 (Aug 2017)

Abstract In recent years, Composite materials have become part of advanced engineering materials, due to their applications and advantages. One of the main considerations when designing composite materials is buckling load. Among the factors affecting critical buckling load, two factors will be discuss here. The aim of this work is to study the effect of different fiber volume fractions (1.25%, 2.5%, 5%, 10%, and 20%) and different beam length on the critical buckling load for beam made from epoxy reinforced by composite. This work was achieved based on simulation and experimental. Buckling load for composite beam is found to be increased with increment of the fiber volume fractions for each length until 5% and decreased gradually up to 20% of volume fraction. These variations in buckling load were due to brittle behavior resulting from the increment of the fiber volume fraction. Beam with small slenderness ratio show high buckling load in compare with high ratio. The numerical results showed a good agreement with the experimental work. Keywords: Epoxy, beam, buckling load, ANSYS Program, volume fractions. 1. Introduction

1 In recent decades, different engineering applications such as aerospace, aircrafts, automobile, marine, civil, and light weight structures use fiber reinforced composite materials. There are several advantages of composite materials such as resistance to corrosion, high strength, weight savings, and impact resistance. Fiber-reinforced composite element are used also as a movable elements like rotating machine parts, robot arms and turbine blades (Muhannad, et al, 2017). (Kunj, et al, 2015) Study the effect of volume fraction of fiber and fiber orientation on critical buckling load for cantilever beam using ANSYS program and compare the results with experimental work. (Jahan and Shahcheragh, 2015) Compute and compare the buckling of thin beam for composite materials, by studying different boundary conditions such as fiber volume fraction, fiber density and dimensions of the beam. Mahmoud (Shariati, et al, 2010) Study the effects of thickness, length, sector, angle and different boundary conditions using numerical and experimental investigation on cylindrical panels to determine buckling load and post- bulking behavior. (Jin and Jeong, 2012) Using test method to determine and detect buckling behavior of composite I-section web reinforced with (E-glass) randomly oriented by verifying finite element analysis with experimental result. (Basharia, et al, 2012)

*Corresponding author’s ORCID ID: 0000-0003-0036-9222

Investigate the fracture and buckling load for glass fiber/epoxy laminated plates using hand lay-up process experimentally. (Jawad, et al, 2014) studied the influence of volume fraction of glass fibers and slenderness ration of beam length on critical buckling load, It was found that the critical buckling load was increased as the volume fraction of glass fiber increased, also, buckling resistance is decreased when beam length is increased. The previous works didn’t show the effect of excessive increase in volume fraction and also beam length is need to study in more details, for that reason this work will be focusing on these two factors. In this paper, critical buckling load for composite beam at different fiber volume fractions (1.25%, 2.5%, 5%, 10%, 20%) with different beam length (70, 140, 200, 290, 385, 400 mm) are studied. Since experimental result had a good agreement when compared with that observed from simulation, so that three beams long are accomplished experimentally and the other one are analyzed based on finite element modeling using ANSYS 11.0 program.

2. Experimental work Experimental studies was conducted for a composite beam with a circular cross section area (D=12.86mm) and different length (70, 200, 385 mm). The tensile test specimen was design based on ASTM D695 which shown in figure (1). These samples are made as a samples of buckling beam from epoxy reinforced by

http://orcid.org/0000-0003-0036-9222

Ali adel battawi Factors affecting critical buckling load of reinforced beam


composite material with different fiber volume fraction. The mechanical properties of composite materials are determined for five samples of fiber volume fractions shown in table (1). These data was used as input data in ANSYS 11.0 program to estimate critical buckling load. A total of 18 specimens test for buckling beam shown in figure (2) are subjected to uniaxial compression load using universal testing machine, Zwick / Roell Z100, figure (3), were composite beam clamped into the clamping zone with a Strain Rate equal to (0.5mrn/min).

Fig.1 Tensile test specimen for composite material according to the ASTM (D695)

Hand (lay-up) process have been used in this investigation represented by Fiber (E- glass) as a reinforcement material which is randomly oriented, while resin of epoxy was utilized as a matrix material. Figure (4) show the stress – strain curves for different fiber volume fraction beams.

Fig.2 Buckling test specimen made by epoxy composite and reinforced by different volume fraction with

different length

Fig.3 Buckling load machine

Table 1 Mechanical properties resulting from tensile test for different fiber volume fraction

Poisson ratio

Young modulus

(GPa)

Ultimate stress (MPa)

Yield stress (MPa)

Volume fraction

0.25 1.323 47.62 44..22 Epoxy 0.256 4..72 27.4. 42.764 1.25% 0.257 4.927 37.04 4...24 2.5% 0.258 4.092 51.51 44.4.0 5% 0.259 4..492 2..6. 49..49 10% 0.26 4.6926 22.24 47..42 20%

Fig.4 The stress -strain curves with different fiber volume Fraction

3. Numerical modeling The numerical method was used based on the finite element method to determine the buckling load of composite beam. The commercial package ANSYS 11.0 was employed, due to its efficient to solve most engineering problems. Numerical models were developed based on mechanical properties and geometrical data obtained from experimental results. Buckling analysis used in this work conducted on composite beam under axial compressive load to locate the critical buckling load at which the beam became unstable. The modeling was performed using element (BEAM 2node 188) which is suitable for analyzing beam structures figure (5).

Fig.5 The finite element model of a circular composite beam

0

10

20

30

40

50

60

0 2 4 6 8 10

Str

ess

(N

/mm

2)

Strain

1.25%

2.50%

5%

10%

20%



The element has six degree of freedom for each node include rotations and translations in x,y, and z directions. The input data were including material properties, loads and boundary conditions which was provided to evaluate the buckling load. Figure (6) shows numerical result of critical buckling load for composite beam using ANSYS 11.0 program.

Fig.6 Critical buckling load for composite beam using ANSYS 11.0 program

3. Result and discussion The present work evaluate the critical buckling load for composite material beam reinforced with different volume fraction of fiber and different beam length. In general, for all cases, the comparison between experimental and numerical results show a good agreement for all beams. So that three beam lengths (7, 20, 38.5 cm) are accomplished experimentally and numerically, while length (14, 29, 40cm) are analyzed using finite element method. Figure (7) show critical buckling load with maximum deformation for each volume fraction of fiber (epoxy, 1.25%, 2.5%, 5%, 10%, 20%) and different beam length (7, 14, 20, 29, 38.5, 40cm), It can be seen that increasing the volume fraction of fiber leading to increase the buckling load until the specimen of 5% volume fraction, and decreased gradually until the specimen of 20%. It is obvious that as percentage of fiber increase the composite beam become stiffer and give high Young's modulus, while for (10% and 20%) fiber percentage observed decreasing in buckling load due to brittle behavior of composite material. This behavior is also demonstrated in the stress – strain curve shown in figure (2).

(a)

(b)

(c)

(d)

(e)

0

200

400

600

800

1000

1200

1400

1600

0.008025 0.006763 0.006618 0.00638 0.006826 0.006892

Cri

tica

l lo

ad

(N

)

Max. deformation (mm)

L=7 cm

epo

x

1.2

5

2.5

5 %

10

20

0

50

100

150

200

250

300

350

400

0.22782 0.019197 0.018787 0.018112 0.019378 0.019565

Cri

tica

l lo

ad

(N)


L=14 cm

epo

xy

1.2

5

2.5

%

5 %

10

%

20

0

20

40

60

80

100

120

140

160

180

0.038863 0.032748 0.032048 0.030895 0.033056 0.033374

Cri

tica

l lo

ad

(N

)


L =20 cm

epo 1.2 2

.5

% 5

%

10

20

0

10

20

30

40

50

60

70

80

90

0.067823 0.05715 0.055929 0.053918 0.057688 0.058243

Cri

tica

l lo

ad

(N

)


L =29 cm

epo

x

1.2

5

% 2

.5

% 5

10

20

0

5

10

15

20

25

30

35

40

45

50

0.103727 0.087404 0.085536 0.08246 0.088227 0.089075

Cri

tica

l lo

ad

(N

)


L =38.5cm

epo

x

1.2

5 %

2.5

5 %

10

%

20

%



(f)

Fig.7 Critical load vs. max. deformation for different fiber volume fraction and different beam length [(a)

L=7cm, (b) L=14cm, (c) L=20cm, (d) L=29cm, (e) L=38.5cm, (f) L=42cm]

It is evident that from figure (7) by increasing the length of the beam, the buckling load slightly decreases. The slenderness ratio was clearly affected the buckling, so beams with small slenderness ratio gave high buckling load while low buckling load observed in high slender ratio. Figure (8) display critical buckling load versus volume fraction of fiber in different slenderness ratios of beam length. Slenderness ratio can be also calculated analytically by (Cameron, 2017):

r

Ls (1)

A

Ir (2)

Where: L: length of the beam. r: radius of gyration. A: cross section area. I: moment of inertia.

Fig.8 The critical buckling load vs. volume fraction of fiber for different slenderness ratios

A summary of the critical buckling load achieved in experimental work compared with numerical results are listed in Table (2) with a maximum deviation do not exceed 14%. Figure (9) show a comparison between experimental and numerical results for Critical buckling loads versus different volume fraction of fiber for the lengths done experimentally.

(a)

(b)

(c)

Fig.9 Comparison between experimental and numerical results for critical buckling load vs. different percentage of volume fraction in beam with different

lengths [(a) L=7cm, (b) L=20cm, (c) L=38.5cm]

0

5

10

15

20

25

30

35

40

45

0.109854 0.02956 0.090582 0.087324 0.093431 0.09433

Cri

tica

l lo

ad

(N

)


L =42cm

epo 1

.25

2.5

5%

10

20

0

200

400

600

800

1000

1200

1400

20% 10% 5% 2.50% 1.25% epoxy

Cri

tica

l lo

ad

(N

)

Volume fraction%

22.04%

44.09%

62.99%

91.33%

121.25%

132.28%

500

600

700

800

900

1000

1100

1200

1300

1400

1500

epoxy 1.25% 2.50% 5% 10% 20%P

cr (

N)

Volume fraction(%)

L=7cm

exp.

num.

0

50

100

150

200

250

epoxy 1.25 2.5 5 10 20

Pcr

(N

)

Volume fraction (%)

L= 20cm

exp.

num.

0

10

20

30

40

50

60

epoxy 1.25 2.5 5 10 20

Pcr

(N

)

Volume fraction (%)

L=38.5 cm

exp

num



Table 2 Critical Buckling load [kN] of different fiber volume fraction for both experimental and numerical simulation

Vf %

L = 7 cm L = 14 cm L = 20 cm L = 29 cm L = 38.5 cm L = 42 cm

Num. Exp. Num. Exp. Num. Exp. Num. Exp. Num. Exp. Num. Exp.

epoxy 882.81 937.71 219.084 - 107.557 124.15 51.206 - 29.065 31.309 26.927 -

%52.1 1243

1320.7 308.549 - 151.48 176.921 72.118 - 40.934 46.629 37.923 -

2.5% 1298

1230.8 322.171 - 158.168 178.952 75.302 - 42.741 44.571 39.597 -

5% 1397

1357.4 346.652 - 170.187 191.934 81.024 - 45.989 51.857 42.606 -

10% 1220

1254.2 302.616 - 148.668 175.35 70.779 - 40.174 42.392 37.219 -

20% 1197

1129.7 297.074 - 145.848 152.92 69.0436 - 39.412 41.151 36.513 -

Conclusions In this paper, a combined of numerical and experimental study is presented to show the critical buckling load for epoxy beam reinforced with random fiber (E-glass). Two factors were chosen for that, volume faction with different percentage (1.25%, 2.5%, 5%, 10%, 20%) and different beam lengths (7cm, 14cm, 20cm, 29cm, 38.5cm, 42cm). Based on the previous results, it can be concluded that: 1) Maximum buckling load was observed at volume

fraction of (5%) as a result of ductility behavior at this percentage, which gave the composite beam ability to absorb more compression loads before failure.

2) It was also observed that by increasing the amount of fiber percentage to 10% and 20%, the buckling load decreased due to the brittle behavior of composite material.

3) Beam with small slenderness ratio gave high buckling load compare with high slenderness ratio.

4) A good agreement between experimental and numerical results was shown, with a maximum deviations less than (14%).

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