A Theoretical and Experimental Approach for Sandwich Composites

A Theoretical and Experimental Approach for Sandwich Composites

Sathyanarayana V.1* , Sharath N2*, Dr. Irfan G3, Swetadri Srinivasan4*,

1,2,3,4 Dept. of Mechanical Engineering, Akshaya Institute of Technology, Tumkur

Abstract – Sandwich composites are becoming more and more popular in structural design, mainly for their ability to substantially decrease weight while maintaining mechanical performance. This weight reduction results in a number of benefits, including increased range, higher payloads and decreased fuel consumption.

It has long been known that separating two materials with a lightweight material in between increases the structures stiffness and strength. So Macro mechanical analysis of sandwich composites is done, Theoretically, modified classical lamination theory (CLT) and mechanics of material (MOM)approach has been used to determine in-plane elastic properties of sandwich composites, Experimentally, sandwich composites were tested to determine in-plane elastic properties, Experimental results are in good agreement with the theoretical values obtained modified CLT and MOM approach.

Keywords: Composites, Elastic Properties, Sandwich

INTRODUCTION

The use of composite sandwich structures in aerospace and civil infrastructure applications has been increasing especially due to their extremely low weight that leads to reduction in the total weight and fuel consumptions. High flexural and transverse shear stiffness and corrosion resistance. In addition, these materials are capable of absorbing large amounts of energy under impact loads which results in high structural crash worthiness. In its simplest form a structural sandwich, which is a special form of laminated composites, is composed of two thin stiff face sheets and a thick light weight core bonded between them. A sandwich structure will offer different mechanical properties with the use of different types of materials because the overall performance of sandwich structures depends on the properties of the constituents. Hence, optimum material choice is often obtained according to the design needs. Various combinations of core and face sheet materials are utilized by researchers worldwide in order to achieve improved crash worthiness.

In a sandwich structure generally the bending loads are carried by the force couple formed by face sheets and the shear loads are carried by the light weight core material. The face sheets are strong and stiff both in tension and compression as compared to the low density core material whose primary purpose is to maintain a high moment of inertia. The low density of the core material results in low panel density; therefore under flexural loading sandwich panels have high specific mechanical properties relative to the monologue structures. Therefore, sandwich panels are

highly efficient in carrying bending loads. Under flexural loading, face sheets act together to form a force couple, where one laminate is under compression and the other under tension. On the other hand, the core resists transverse force sand stabilizes the laminates against global buckling and local buckling. Additionally, they provide increased buckling and crippling resistance to shear panels and compression members.

Modeling composite Sandwich Structures

Mechanics can be divided into three major areas

a) Theoretical b) Applied c) Computational

Theoretical mechanics is concerning about fundamental laws and principles of mechanics. Applied mechanics uses this theoretical knowledge in order to construct mathematical models of physical phenomena and to constitute scientific and engineering applications. Lastly, computational mechanics solves specific problems by simulation through numerical methods on computers.

According to he physical scale of the problem, computational mechanics can be divided into several branches:

a) Nano mechanics and micromechanics b) Continuum mechanics c) Systems

Nanomechanics deals with phenomena at the molecular and atomic levels of matter and microcechanics concerns about crystallographic and granular levels of matter and widely used for technological applications in design and fabrication of materials and microdevices. Continuum mechanics is used to homogenize the microstructure in solid and fluid mechanics mainly in order to analyze and design structures. Finally systems are the most general concepts and they deal with mechanical objects that perform a noticeable function.

As it is the issue of this study, the modeling of composite materials is more complex that of traditional engineering materials. The properties of composites, such as strength and stiffness, are dependent on the volume fraction of the fibers and the individual properties of the constituent materials. In addition, the variation of lay-up configurations of composite laminates allows the designer greater flexibility but complexity in analysis of composite structures. Likewise, the damage and failure in laminated composites are very complicated compared to that of conventional materials. Due to these aspects, modeling of composite laminates is investigated as macro-mechanical modeling

Macro-mechanical modeling

Classical lamination theory for thick laminates

In the classical lamination theory, it was assumed that the laminate is thin compared to its lateral dimensions and that straight lines normal to the middle surface remain straight and normal to that surface after deformation. As a result,

xy

yx

A12 A22

A12 A

the transverse shear stress xz , yz and shear strains 11

xz ,yz are zero. These assumptions are not valid in the case of thicker laminate and laminates with low stiffness central plies undergoing significant transverse deformations. In the theory discussed below, referred to as first order shear deformation laminated plate theory, the assumption of normality of straight lines is removed, and that is, straight lines normal to the middle surface remain straight but not normal to that surface after deformation.

Figure 5.4 thick sandwich composite plates and E-glass epoxy laminate

Figure 5.5 shows a section of a laminate normal to the y- axis before and after deformation, including the effects of transverse shear. The result of the latter is to rotate the cross-section A by an angle x to a location A, which is not normal to the deformed middle surface.

xy = Longitudinal Poisons ratio of sandwich composite

yx = Transverse Poisons ratio of sandwich composite

G A66

xy h

Gxy = In plane shear modulus of sandwich composite

Table 5.6 Macro mechanical properties of sandwich composites

Characterization of sandwich composite laminate using mechanics of material approach

Tensile modulus of sandwich composite can be determined by using strength of materials approach.

Fig 5.6. Sandwich composite in Mechanics of material approach

2Ef Af Ec Ac

Esandwich

Or

2Af Ac

Fig 5.5: The relationship between displacements through the thickness of a plate to midplane displacements and curvatures.

Esandwich EFs VFs ECore Vcore

A A2 Ex 11 22 12

hA22

A A A2 Ey 11 22 12

hA11

Ex = Longitudinal Youngs modulus of sandwich composite

Ey = Transverse Youngs modulus of sandwich composite

Ef = youngs modulus of fiber Em = youngs modulus of matrix Af = Area of fiber

Ac = Area of core

VFs = Volume fraction of face sheet Vcore = Volume fraction of core

Table 5.7 properties of sandwich composites by mechanics of materials

approach

EXPERIMENTAL

3 COMPOSITE SANDWICH STRUCTURE

1. Tensile test

   In-plane tensile tests were conducted to determine the tensile strength and modulus characteristics of the

   Where the 1 and 2 is the strain measured by the +450 gauge and the strain measured by the 450 gauge. The average shear stress is then determined by dividing the applied load P by the area of the cross section between the notches.

   P

   composite sandwich panels. Forth is purpose, tensile test specimens were sectioned from larger composites and wich panel and tests were performed using them echanical

   avg 2 A

   (4.12)

   (UTM) test machine at a crosshead speed of 0.5 mm/min. Figure 4.18 shows the geometry and test configuration of tensile test specimen Load versus deformation values was recorded during testing.The tensile strength and modulus

   The apparent shear modulus is then calculated by dividing the average shear stress by the average shear strain:

   avg

   values were obtained by equations 3. 3 and 3.5 similarly with the face skin material.

   Gavg

   avg

   (4.13)

   (a)

   (b)

   Figure 4.18 Sandwich test specimen (a) Geometry of the specimen (b) Actual specimen

   Shear block as shown in figure 4.17(a)

   Was used for the testing of sandwich composite specimens

   (a)

2. Shear test

The shear tests were conducted to determine the in plane and out of plane loading effects on shear properties of sandwich composite specimens. The details of the specimen for shear test are shown in figure 4.18. The specimen was loaded in a universal testing machine by shear test xture at a constant head speed of 1 mm/min. Three for each specimen type were provided with resistance strain gauges oriented at ±450 to the loading axis and bonded in the middle of the specimen to determine its shear response during the entire loading regime. The average shear strain is then determined from the strain gauges using the relation

(b)

Figure 4.18 Sandwich shear test specimen (a) Geometry of the specimen

(b) Actual specimen

RESULTS AND DISCUSSION

Tensile test of Sandwich composites

The Youngs modulus and poisons ratio are obtained from the slope of the initial portion of stressstrain plots and lateral and linear strain plots as shown in figure 6.5 and

6.6. The predicted and experimental values of elastic properties are shown in Table 6.4 and 6.5. The elastic moduli predicted by modified CLT and mechanics of

avg 45 45

(4.11)

material showed good agreement.

50

Stress, MPa

Stress, MPa

40

30

20

10

0

0 0.005 0.01

Strain

SF SFK20 SFK15 SFK10 SFK5

Table 6.6 comparing the theoretical results with experimental results of sandwich composites

Figure 6.5 Stress versus strain plot of sandwich composite

600

Lateral strain

Lateral strain

500

400

300

200

100

0

0 1000 2000 3000 4000

Linear strain ×10-6

Figure 6.6 Linear versus Lateral strain plot

6.3.1 Failed specimen of Sandwich composite

Figure 6.7 Failed specimens of Sandwich composite Table 6.5 Experimental Results of Sandwich composites

From the figure 6.5 we can see that as Honeycomb cell size decreases the load taken by the sandwich composite is high. Therefore honeycomb structure and the cell size of that plays an important role in the tensile strength of sandwich composite. Failure occurs in the tensile test causes the cursing f Kraft honeycomb core resulting in delamination at the edges of the sandwich. The maximum average load which can be withstand by sandwich composite is SFK 5 15.450 KN.

In plane shear test on sandwich composite

The shear modulus is obtained from the slope of the initial portion of stressstrain plots shown in figure 6.10. The predicted and experimental values of elastic properties are shown in Table 6.7 and 6.8. The elastic moduli are predicted by modified CLT and mechanics of material showed good agreement.

25

Stress, Mpa

Stress, Mpa

20

15 SF IP

10 SFK20 IP

SFK15 IP

5 SFK10 IP

0 SFK5 IP

0 20000 40000

Strain

Figure 6.10 Stress versus strain plot of in plane shear test sandwich composite

Figure 6.11 Failed specimen of in plane shear test

Table 6.8 Experimental Results of In plane shear test on Sandwich composites

Table 6.9 comparing the theoretical results with experimental results

The maximum applied load under in plane shear test of composite sandwich is 27.376KN for SFK 5 shows the honeycomb structure and the cell size of that plays an important role in the shear strength of sandwich composite. Table 6.8 summarizes the predicted and the measured Shear modulus of the composite sandwich under In plane shear test. The predicted and the actual Shear modulus of the Sandwich using the in-plane shear equation are nearly equal. The presence of the fibre composite skins adds to the overall strength of the specimen by preventing the widening of the crack in the core material and delayed the shear failure until all the fibres crossing the cracked core failed.

CONCLUSION

1. Modified classical lamination theory was developed for thicker laminate and laminates with low stiffness central plies undergoing significant transverse deformations.

2. Using Modified classical lamination theory, elastic properties of sandwich composites are calculated.

3. The experimental investigations are carried by conducting different test for the Sandwich composite, to find the elastic properties of the material.

4. For Sandwich composite, Experimental results are in good agreement with the theoretical values obtained Modified classical lamination theory and Mechanics of material approach.

5. Therefore, separating two materials with a lightweight material in between increases the structures stiffness and strength.

REFERENCES

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