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ANALYSIS OF COMPOSITE LEAF SPRINGS

by

Erdoğan KILIÇ

March, 2006

İZMİR

ANALYSIS OF COMPOSITE LEAF SPRINGS

ABSTRACT

In this study, the bearing strength, failure mode, failure load of glass fiber-epoxy

composite leaf spring with four circular holes which are subjected to tensile force are

investigated experimentally and numerically. The end distance to diameter (E/D) and width

to diameter (W/D) ratios in the leaf spring were changed from 1 to 4 and 4 to 5 respectively.

The numerical study is performed by using 3D FEM with assistance of LUSAS 13.6 finite

element analysis program.

Keywords: Composite materials, composite leaf springs, failure analysis.

KOMPOZİT MALZEMEDEN YAPILAN

YAPRAK YAYLARIN ANALİZİ

ÖZ

Bu çalışmada çekme kuvvetine maruz kalan dört delikli glass fiber/epoksi yaprak yayın

yatak mukavemeti, hasar çeşidi ve hasar yükü deneysel ve nümerik olarak araştırılmıştır.

Yaprak yayın deliğin köşe uzaklığının delik çapına oranı (E/D) 1’den 4’e kadar ve yaprak yay

genişliğinin delik çapına oranı (W/D) 4’den 5’e kadar değiştirilmiştir. Nümerik çalışma

LUSAS 13.6 sonlu eleman analiz programı yardımı ile gerçekleştirilmiştir. Ve daha sonrada

deneysel sonuçlar ve nümerik tahminler karşılaştırılmıştır.

Anahtar sözcükler : Kompozit malzeme, kompozit yaprak yaylar, hasar analizi.

1. Introduction

Composite materials are now used extensively in the leaf spring applications to take the

place of metals. Fiber reinforced plastics can withstand stresses and elastic deformation to a

level that enables the same amount of elastic energy to be stored per unit of volume as in the

best spring steel.

When composites are used as structural materials, it is necessary to join composites to

other materials. There are two types of joints: mechanical and adhesively bonded joints.

Mechanical joints are easy to dismantle for repair and inspection. Also mechanical joints are

preferred for their simplicity and low cost. However mechanical joints causes stress

distribution around holes.

Many investigators have strength of mechanically fastened joints in composite structures.

Lim et al studied the fatigue characteristics of the bolted joints for unidirectional composite

laminates. They investigated fatigue characteristics of laminate bolted joints with respect to

the angle θ and the bolt clamping pressure and compared with the result of laminate. Ireman

has developed a three dimensional finite element model of bolted composite joints. In that

work an experimental program has been conducted to measure deformations, strains, and bolt

load on test specimens for validation of the numerical model developed. İçten and Karakuzu

have investigated the failure strength and failure mode of a pinned-joint carbon-epoxy

composite plate of arbitrary orientations. They analyzed the failure load and failure mode

numerically and experimentally. Shokrieh and Rezai investigated analysis and optimization

of a composite leaf spring. In that study the objective was to obtain a spring with minimum

weight that is capable of carrying given static external forces without failure.

In this study the bearing strength, failure mode, failure load of glass fibre-epoxy composite

leaf spring with four circular holes which are subjected to tensile force are investigated

experimentally and numerically. The three dimensional finite element method is used to

determine the failure load and failure mode using Hashin failure criteria. The bi-directional

glass fiber-epoxy composite leaf springs were produced and standard tests were performed to

obtain mechanical properties.

2. Problem definition

In this study the composite plates were considered to use at vibrating conveyor.(Fig.1)

1420 rpm electric motor driven crank shaft at a transmission rate of 0,4.Composite plate is

mounted between crank shaft and machine table.(Fig.2) Four M10 bolts were used to clamped

te composite plates. Fig.3 shows a typical configuration and definition of composite leaf

spring. The length of leaf spring is denoted by L, width is denoted by W. Hole of diameter D

is at a distance E form free edge of leaf spring. The hole diameter (D) was fixed at a constant

value of 10 mm.

Fig 1. Vibrating conveyor

Fig.2 Detail of composite plate mounting.

Typical failure modes of mechanically fastened joints under tensile loads are classified into

net tension mode, shear-out mode and bearing mode. These modes are shown in Fig.4. In

practice combinations of these failure modes are possible. Four groups of parameter influence

the behavior of joint:

• Material parameters: Fiber form and type, fiber orientation, resin type, laminate

stacking sequence etc.

• Design parameters: Loading direction, failure criteria, loading type.

L

E

E

DD

W

• Geometry parameters: specimen width (W), ratio of width to hole diameter (W/D),

edge distance (E), ratio of edge distance to hole diameter (E/D), hole size (D),

thickness (t).

• Fastener parameters: hole size, clamping area, fastener type.

Fig.3 Geometry of a composite leaf spring

In this study ratio of distance to hole diameter (E/D) and ratio of width to hole diameter in

the leaf spring are changed form 1 to 4 and 4to 5 respectively for ± 45° and 0°-90° fiber

orientation. Leaf spring was fastened by M10 bolts. The load is parallel to the leaf spring

and is a symmetric with respect to the center line. The bearing strength of a hole is

represented as follows:

tD

P

..2=σ (1)

Where P is ultimate failure load, D is diameter of hole and t is thickness of leaf spring.

3. Production of composite leaf spring

The fiber reinforced composite material used in this study was produced in Izoreel

Composite Isolate Materials Company. E-glass fiber and epoxy resin were used to

manufacture the specimens. Glass fiber and epoxy are cured for 4 hours at 130 ° C. The

composite composite plate consist four symmetric layers [0/90]4S. At the end of

manufacturing the thickness of material was measured as 3 mm.

Fig.4 Failure modes of fibrous composite mechanical joints

Fig.5 The fiber direction of the structure

4. Experimental study

Mechanical tests were performed to determine the mechanical properties. To find E1 and

ν12 two strain gauges were stuck on a specimen. One of them was in the loading direction and

the other was transverse direction. The specimen was loaded step by step to rapture by Instron

tensile testing machine of 20 kN capacity at ratio of 0.5 mm/min. for all steps ε1 and ε2 were

measured. By using these strains E1 and ν12 were obtained. Xt calculated by dividing ultimate

force by cross-sectional area of specimen under tensile loading.

To obtain the shear modules G12 , a specimen whose principal axis was on 45° was taken

and a strain gauge was stuck on loading direction of lamina. The specimen was loaded step by

step up to rupture by the testing machine. For all steps εx was measured by indicator. By using

this strain G12 was calculated as follows:

21

12

1

12 1214

1

EEEE

G

x

−+−

=ν

(2)

Because of the small thickness G13 and G23 are assumed to be equal to G12.

To define the shear strength S Iosipescu testing method is used.(Fig.6) The dimensions of

specimen were chosen as a = 80 mm, b = 20 mm, c = 12 mm and ti = 3 mm. A compression

test was applied to the specimen. In failure, S is calculated from:

ct

FS

i .

max= (3)

Where Fmax is the failure force.

The mechanical properties of glass-epoxy composite leaf spring which were obtained from

the standard test have been given in Table 1.

Fig.6 Iosipescu test fixture

P P

In order to find failure load and failure mode, a series of experiment were performed. The

effects of bolt location and fiber direction were studied by varying the width to diameter

(W/D) and edge distance to diameter (E/D) ratios , from 1 to 4 and 4 to 5, respectively, for the

0°-90° and ± 45° fiber orientation angles while keeping D, t and L constant.

The experiments were carried out in tension mode on Instron Tensile Machine at a

crosshead speed of 0.5 mm/min. The M10 bolt with class 12.9 was used for bolted specimens.

Schematic diagram of loading fixture is shown Fig.7

Table 1.Mechanical properties of the glass epoxy composite

E1=E2 (MPa) G12 (MPa) ν12 Xt = Yt (MPa) Xc = Yc (MPa) S (MPa)

23070 4630 0,05 398 313 77

Fig.7 Shematic diagram of the loading fixture

For each type of composite joint, three tests were conducted and the average bearing

strength values were calculated.

5. Finite Element Analysis

Finite element analysis was used to study the behavior of joints and predict the failure load

and failure mode. The FE analyses were carried out using the FE system LUSAS 13.6

version. Typical meshes of leaf spring are shown in Fig.8. The mesh is divided to major

regions, a square area with a fine mesh surrounding the bolt hole and rectangle with a coarser

mesh away from the bolt hole. The problem is defined materially linear and geometrically

nonlinear. Hashin failure criteria is used in the failure analysis. Each ply in the laminate was

modeled using Composite Brick Element (HX16L) which has hexahedral shape and quadratic

interpolation order. Symmetry was adopted along the length of the joint and thus the model

was reduced to half model as shown in Fig.8. The fixed hole surface of the leaf spring is

supported in radial direction. After that tensile load was applied the free hole. The analyses

were performed as nonlinear load increment.

Fig.8 Finite element model of the composite leaf spring.

Detail A Detail B

Symmetry plane

0

500

1000

1500

2000

2500

3000

0 1 2 3 4 5 6 7

displacement(mm)

Lo

ad

(N)

E/D=1

E/D=2

E/D=3

E/D=4

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5 6 7 8 9

displacement(mm)

Lo

ad

(N) E/D=1

E/D=2

E/D=3

E/D=4

6. Result and discussion

Every specimen was loaded until tear occurred. The general behavior of the composite was

obtained from the load/displacement curves. In this study, three basic failure modes were

observed. Some specimen tears immediately. This failure mode corresponds to net-tension

modes which is weakest and most dangerous mode. For some other specimen the load

decreases with increasing bolt displacement and then specimens tear.

Fig. 9. Load-displacement curves for glass epoxy leaf spring (θ = ± 45° W/D=4)

Fig. 10. Load-displacement curves for glass epoxy leaf spring (θ = ± 45° W/D=5)

θ=±45°,W/D=4

θ=±45°,W/D=5

0

1000

2000

3000

4000

5000

6000

7000

0 1 2 3 4 5 6 7 8 9 10 11 12 13

displacement(mm)

Lo

ad

(N)

E/D=1

E/D=2

E/D=3

E/D=4

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1 2 3 4 5 6 7 8 9 10 11 12

displacement(mm)

Lo

ad

(N)

E/D=1

E/D=2

E/D=3

E/D=4

This failure mode corresponds to shear out mode. The load increases with increasing

deformation and finally reaches an ultimate level. Following this, the load decreases with

increasing deformation. But specimen continues to sustain to load. This failure mode

corresponds to bearing mode

The bearing strength increases with increasing E/D ratio for θ = ± 45° and W/D = 4. The

failure mode is net-tension and shear out for E/D = 1. The failure mode changes to net tension

for E/D = 1,2,3,4.

Fig. 11 Load-displacement curves for glass epoxy leaf spring

(θ = 0°-90° W/D=4)

Fig. 12. Load-displacement curves for glass epoxy l eaf spring

(θ = 0°-90° W/D=5)

θ=0-90°,W/D=4

θ=0-90°,W/D=5

For θ = 0°-90° and W/D = 4 the critical E/D ratio is 4. The bearing strength decreases for

E/D= 4. The failure mode is shear out for E/D = 1,2 while it becomes bearing for E/D = 3,4.

For θ = ± 45° and W/D = 5 the critical E/D = ratio is 4. In the case of W/D = 4 the bearing

strength decreases.

Fig. 13. The effect of E/D ratio on the bearing strength ( W/D=4)

Fig. 14. The effect of E/D ratio on the bearing strength ( W/D=5)

Bearing strengths increase by increasing the W/D ratio while E/D ratio is held constant.

Bearing strengths are approximately two times greater for θ = 0°-90° than θ = ± 45°. All

0

20

40

60

80

100

120

140

0 1 2 3 4 5E/D

Beari

ng

str

en

gth

(Mp

a)

0-90 experimental 45 experimental

0-90 numerical 45 numerical

0

20

40

60

80

100

120

0 1 2 3 4 5E/D

Be

ari

ng

str

en

gth

(M

pa

)

0-90 experimentall 45 experimental

0-90 numerical 45 numerical

W/D=4

W/D=5

failure modes and failure loads result of experimental and numerical study are presented in

Table 2.

Table 2. Comparisons of numerical and experimental failure modes and failure loads of the glass epoxy

leaf spring ( N = net-tension mode, S= shear-out mode, B= bearing mode)

The specific examples of finite element analysis are shown from Fig 15 to Fig.30

Failure mode Failure load ( N)

W/D =4 θ 0 Experimental Hashin Experimental Hashin

0-90 S S-N 5303 3810 E/D=1

± 45 S-N N 2248 1532

0-90 S N 5522 4004 E/D=2

± 45 N N 2394 1688

0-90 B B 6385 4142 E/D=3

± 45 N N 2540 1704

0-90 B N 6112 3914 E/D=4

± 45 N N 2846 1734

W/D=5 θ0

0-90 S S 5415 3834 E/D=1

± 45 S-N N 2316 1642

0-90 S S 5722 4968 E/D=2

± 45 B-N N 2966 2226

0-90 B B 7003 5324 E/D=3

± 45 B-N S-N 3326 2246

0-90 B N 6811 5054 E/D=4

± 45 B-N N 3082 2240

Fig 15 E/D=1, W/D=4 θ = ± 45°

Pmax = 1532 N failure mode : net tension

Fig 16 E/D=2, W/D=4 θ = ± 45°

Pmax= 1688 N failure mode : net-tension

Fig17 E/D=3, W/D=4 θ= ± 45°

Pmax = 1704 N failure mode : net-tension

Fig.18 E/D=4, W/D=4 θ = ± 45°

Pmax = 1734 N failure mode : net-tension

Fig.19 E/D=1, W/D4 θ = 0°-90°

Pmax = 3810 N failure mode: net-tension

and shear out

Fig.20 E/D=2, W/D=4 θ = 0°- 90°


Fig.21 E/D=3, W/D=4 θ = 0°- 90°

Pmax = 4142 N failure mode: bearing

Fig.22 E/D=4, W/D=4 θ = 0°- 90°


Fig.23 E/D=1, W/D=5 θ = ± 45°

Pmax =1642 N failure mode: net-tension

and shear out

Fig.24 E/D=2, W/D=5 θ = ± 45°


Fig.25 E/D=3, W/D=5 θ = ± 45°

Pmax =2246 N failure mode: net-tension

and shear out

Fig.26 E/D=4, W/D=5 θ = ± 45°


Fig.27 E/D=1, W/D=5 θ =0°-90°

Pmax = 3834 N failure mode: shear out

Fig.28 E/D=2, W/D=5 θ =0°- 90°

Pmax = 4968 N failure mode: shear out

Fig.29 E/D=3, W/D=5 θ =0°-90°

Pmax = 5324 N failure mode: bearing

Fig.30 E/D=4, W/D=5 θ =0°-90°

Pmax = 5054 N failure mode: net tension

Fig.31. E/D=1, W/D=4 θ= ± 45° Pmax =2248 N failure mode: net tension

and shear out

Fig.32 E/D=2, W/D=4 θ= ± 45° Pmax = 2394 N failure mode: net tension

Fig.33 E/D=3, W/D=4 θ= ± 45° Pmax = 2540 N failure mode: net tension

Fig.34.E/D=4, W/D=4 θ= ± 45° Pmax = 2846 N failure mode: net tension

Fig.35. E/D=1, W/D=4 θ= 0 - 90° Pmax = 5303 N failure mode: shear out

Fig.36. E/D=2, W/D=4 θ = 0-90° Pmax = 5522 N failure mode: shear out

Fig.37 E/D=3, W/D=4 θ= 0-90° Pmax = 6385N failure mode: bearing

Fig.38 E/D=4, W/D=4 θ=0-90° Pmax = 6112 N failure mode: bearing

Fig.39 E/D=1, W/D=5 θ= ± 45° Pmax = 2316 N failure mode: net-

tension and shear out

Fig.40 E/D=2, W/D=5 θ= ± 45° Pmax = 2966 N failure mode: net-

tension and bearing

Fig.41 E/D=4, W/D=5 θ= ± 45° Pmax= 3082 N failure mode: net-

tension and bearing

Fig.42 E/D=1, W/D=5 θ= 0-90° Pmax = 5415 N failure mode: shear-out

Fig.43 E/D=2 W/D=5 θ= 0-90° Pmax = 5722 N failure mode: shear-out

Fig.44 E/D=3 W/D=5 θ=0-90° Pmax = 7003 N failure mode: bearing

Fig.45 E/D4 W/D=5 θ=0-90° P max = 6811 N failure mode: bearing

7. Conclusion

Bearing strength and failure modes of E-glass/ epoxy leaf spring are investigated

numerically and experimentally. In numerical study Hashin failure criteria are used to predict

the failure load and failure mode. Also the effect of different geometries and fiber orientations

are observed.

From the experimental and numerical results presented it can be concluded that:

1. For θ = 0°-90° and W/D = 4 the critical E/D ratio is 4. The bearing strength decreases for

E/D = 4.

2. For θ = ± 45° W/D = 5 the critical E/D ratio is 4. In the case of E/D = 4 bearing strength

decreases.

3. The bearing strength increases with increasing E/D ratio for θ = ± 45 and W/D = 4.

4. The bearing strength of composite leaf spring has the maximum value for θ = 0°-90°,

W/D= 5 and E/D = 3.

5. The bearing strength are approximately two times greater for θ = 0°-90° than θ = ± 45°.

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