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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°
Pmax = 4004 N failure mode: net-tension
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°
Pmax = 3914 N failure mode: net-tension
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°
Pmax = 2226 N failure mode: net-tension
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°
Pmax = 2240 N failure mode: net-tension
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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