MECH70 Final Report_FOR LINKEDIN

STRUCTURAL ANALYSIS AND DESIGN OF A COMPOSITE SPRING
Stephen Roper (0swkr@queensu.ca), K. Pilkey
MECH 470 | Deformation Processing
Department of Mechanical and Materials Engineering | Queen’s University, Kingston, Ontario, Canada
Submitted Tuesday April 26th
2016
Abstract: The Queen’s Space Engineering Team is competing in the 2016 University Rover Challenge,
designing and testing a remote-operated Mars rover to complete various simulated mission tasks. In order to
manoeuver over harsh terrain and complete challenges quickly and smoothly, QSET is designing a novel
Loop-Wheel system that incorporates suspension directly into the outer hoop offering greater stability and
vibration damping characteristics. This research project investigates the design and analysis of elliptical
composite springs for use on the Loop-Wheel, specifically linking laminate microstructure to system
behaviours and failure modes. The final result is a manufacturable design that includes a ten-ply layup,
ellipticity ratio of 0.82 and a radius-to-thickness ratio of 65:3 to maximize energy absorption characteristics
and offset failure mechanisms. The final proposed design offers a maximum deflection of 14.5mm and is
made from unidirectional S-Glass/epoxy constituent materials with cross-ply lamina to help prevent
microcracking, crazing, delamination, microbuckling, and fracture failure modes.
Key Words: fiber reinforced polymer, composite, fiber, matrix, spring, microstructure, delamination, micro
cracking, microbuckling, splitting, HyperWorks, OptiStruct, HyperMesh, HyperView.
NOMENCLATURE
QSET Queen’s Space Engineering Team
URC University Rover Challenge
ERC European Rover Challenge
FRP Fiber Reinforced Polymer
DOF Degrees of Freedom
FE Finite Element
FEA Finite Element Analysis
U Material Strain Energy
σ
Ultimate Tensile Strength (matrix, fiber,
composite).
E Young’s Modulus (matrix, fiber, composite).
ρ Density (matrix, fiber, composite).
V Volume Fraction (matrix, fiber, void).
Wmicro Macro energy dissipation effects.
Wmacro1
Macro energy dissipation effects for 𝑎𝑎/𝑏𝑏 <
0.8, 1, 1.25 (ellipticity ratio).
Wmarco2
Macro energy dissipation effects for 𝑎𝑎/𝑏𝑏 > 1.5
(ellipticity ratio).
ILSS Interlaminar Shear Strength.
ILSSr
𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 of the composite with voids relative to an
equivalent void-free composite.
PSHELL
HyperWorks element type for plane stress
condition.
MAT8
HyperWorks material definition for orthotropic
conditions.
1 INTRODUCTION
Fiber reinforced composites are becoming an increasingly
popular material for industrial, commercial and specialized
applications due to their lightweight properties, high
customizability and long-term durability. Designers across
multiple disciplines are now leveraging FRPs to reduce mass,
readily tailor mechanical properties and improve fatigue
resistance in structural applications under tension, compression
and shear loading. For example, fiber reinforced composites are
being more extensively used in the aerospace industry for critical
components and structures in flexural applications. Currently,
the Boeing 777X series boasts the longest wing design to
incorporate FRPs that are designed to bend during flight for
maximum lift and cruising efficiency [1]. This comes with the
added benefits of lightweighting and low fatigue characteristics
to improve payload, range and operational costs of the aircraft.
In the automotive industry composite materials are also being
incorporated into suspension systems, designed for superior
vibrational damping and lightweight performance. By utilizing
high-strength material properties in unique configurations
composite spring systems are capable of storing recoverable
mechanical energy more effectively compared to conventional
metallic coils [2]. This offers a lightweight, fatigue resistant
spring replacement that allows for smooth movement over
obstacles under repeated dynamic loading.
This significance can be extended into non-conventional vehicle
suspension systems for harsh terrain applications, and in this
case, applied to the Queen’s Space Engineering Team (QSET)
Mars rover. The Queen’s Space Engineering Team competes
annually in the University Rover Challenge (URC), designing,
building and testing a remote-operated vehicle to complete
various mission tasks. One of the main competition challenges is
terrain crossing, where the rover must maneuver over uneven
landscapes and withstand natural obstacles such as steep
inclines, voids, and vertical drops. To enhance vehicle
performance and capability for this challenge QSET is designing
and implementing a novel Loop-Wheel concept that integrates
suspension directly into the outer wheel hoop, offering greater
stability, superior impact resistance and improved vehicle

Stephen Roper
2 Copyright © 2016 by Queen’s University
dynamics. The primary components of the Loop-Wheel design
are the elliptical springs which flex and deform to dampen
vibrations; this research project will investigate the use of fiber-
reinforced polymer composites as these elliptical springs. See
Figure 1 for the initial design concept.
Figure 1: QSET Loop-Wheel concept. Note the placement of the semi-elliptical
loop springs and how they’re joined to the structure.
The University Rover Challenge will take place at the Mars
Desert Research Station in southern Utah, May 2016. QSET has
also entered the European Rover Challenge for the first time
which will take place in Poland, September 2016. Both events
are sponsored by the Mars Society.
1.1 Literature Review
Previous research studies have examined the application of
composite laminates for automotive leaf springs. For example,
one case study tested the suitability of glass fiber composites to
replace the steel leaf spring used in an off-road vehicle (Jeep)
[3]. The analysis was conducted by first reviewing spring theory
to describe how energy is stored and released, referring
specifically to material strain energy, given by Equation 1 [3].
U =
𝜎𝜎2
𝜌𝜌𝜌𝜌
(1)
This suggests that a material with a low density and low modulus
are desired when designing energy absorbing components and
it’s these properties that can be readily tailored in the laminate
construction. The case study suggests a parabolically tapered leaf
spring geometry with a constant-width beam section made from
a woven roving glass/epoxy laminate. In this application the
composite spring successfully minimized mass, increased
corrosion resistance and increased durability but mentioned the
challenges such as sensitivity to manufacturing.
A second case study continued to investigate composite leaf
springs for automotive applications, but focused on the design
optimization of the laminate layup. This paper highlighted the
importance of designing the spring geometry and ply angles to
utilize fiber strength in the principal direction instead of shear to
avoid debonding and delamination failure [4]. Finite element
analysis was applied to determine the ideal spring geometry and
investigated the combined effects of laminate thickness, fiber
orientation and stacking sequence using manual optimization
methodology. The final results from this analysis indicated the
importance of ellipticity ratio on spring rate and life expectancy
of the system, which showed superior fatigue behaviour than
conventional coil springs [4].
1.2 Objectives
The previous research conducted in this field primarily studied
the performance of semi-elliptical composite leaf springs with
predetermined geometry and laminate layups. While the overall
results from each case study provided recommendations on
semi-elliptical spring design they did not include a holistic
investigation into the microstructure, deformation characteristics
and related failure modes for continuous elliptical springs. This
research focuses on spring design and includes an analysis of
laminate design, material properties, geometry, and failure
modes, linking microstructure to characteristic system
behaviours. This spring design analysis addresses three main
objectives:
(a) Laminate design and constituent material properties, to
develop a microstructure that achieves the desired
mechanical properties while avoiding typical failure modes.
(b) Spring geometry, to propose a suitable composite spring
with sufficient energy absorbing characteristics.
(c) Composite failure, to design against the onset of
microcracking, microsplitting, delamination, and
microbuckling in tension, compression and shear loading.
The culmination of this work is a final design recommendation
considering structural geometry and FRP laminate layup
(microstructure). Also suggested are applications for future work
and investigation as well as brief comments on
manufacturability. FE analysis was conducted using Altair
HyperWorks and the OptiStruct, HyperView and HyperMesh
modules.
2 DETAILED INVESTIGATION
2.1 Laminate Design and Material Properties
Laminate structures are highly customizable, and offer the
unique advantage to design the final material microstructure with
specific mechanical properties [5]. Of particular importance to
this project are how different microstructural arrangements can
correspond to energy absorption and failure mechanisms in
bending; in elliptical springs this includes the tension,
compression and shear surfaces. By carefully designing the
laminate stack and choosing appropriate constituent materials
the multiphase structure can be designed to offset specific modes
of failure in flexure with highly predictable in-service behaviour
[5].
First, the fiber matrix layup must be considered to regulate the
structural stiffness and the development of distributed micro
cracks in flexure. This failure mode is typically seen in semi-

Stephen Roper
elliptical springs and can be regulated intrinsically by the
geometry of the material microstructure [5]. These microcracks
and subsequent delamination fracture initiate to dissipate strain
energy and must be considered for spring applications [5].
Next, constituent material properties must be examined for their
influence on the load-deformation characteristics and impact on
failure modes. Properties such as matrix/fiber Young’s modulus
are known to drive changes in failure mode between cooperative
fibre microbuckling to delamination splitting microbuckling [6].
Similar analysis has indicated that bending strength can be
significantly affected by laminate shear strength, dependent on
the interfacing bond strength and compatibility between fiber-
matrix constituent materials [6].
2.1.1 Laminate Design
First, various commercially available fiber fabrics are available
for laminate applications, offering may different microstructural
arrangements for structural applications such as plain, twill and
unidirectional weaves. Stacking angles are usually limited to 0°,
90°, and ±45° fiber orientations in composite design, and depend
on the desired structural properties and recommended
manufacturing practices. In composite springs, laminates
typically consist of unidirectional fabrics arranged in the
longitudinal (circumferential) direction. This provides
preferential support during uniaxial tension and compression;
however, in order to provide resistance to offset loads, such as
torsion, cross-plies can be introduced [7]. This helps make the
spring system more reliable in real-world multi-loading cases.
Laminate thickness and fiber-matrix volume fraction are
additional common design variables for controlling system
mechanical properties. This is achieved by adjusting the number
of plies in the system, with many spring applications using
between five and ten individual lamina [3] [4] [8]. While
laminate thickness controls mechanical properties fiber volume
can be correlated to laminate failure mechanisms. For example,
it has been shown that as volume fraction exceeds 10-20%, the
composite fails through in-phase buckling at a failure stress equal
to the composite shear modulus [6].
This investigation ultimately revealed the high customizability
of laminated structures and their ability to achieve different
mechanical properties from the same base materials. These
considerations can be directly used in design the QSET Loop-
Wheel, suggesting unidirectional fabric with added cross-plies to
offset failure. A sample laminate is provided in Figure 2.
Figure 2: Typical laminate definitions: (a) unidirectional stack (b) 0°-90°
laminate stack [8].
2.1.2 Constituent Materials
While the constituent materials can be arranged to achieve
different mechanical properties it is also important to understand
the individual material properties and their influence on system
behaviour.
Of particular importance for flexural applications is the Young’s
modulus of the matrix constituent material. For example, it has
been found that composite springs experience a significant
increase in bendability with increasing matrix modulus [6]. This is
due to extended elastic deformation and the resultant higher
interfacial bond strength prior to the onset of matrix spalling or
microcracking. The composite Young’s modulus can also act as a
sufficient predictor for the onset of specific failure mechanisms. One
study showed the respective failure modes for three different
composite systems using different matrix materials. The results
from this study showed that an increase in the matrix Young's
modulus leads to a transition from cooperative fibre
microbuckling to delamination splitting microbuckling failure
modes [6]; these results are summarized in Figure 3.
Figure 3: The effect of matrix Young’s modulus on failure mode: (a) low
matrix modulus with cooperative microbuckling in two planes, (b) medium
matrix modulus with only in-plane cooperative microbuckling and (c) high
matrix modulus with delamination splitting microbuckling [6].
Referring to Figure 3 (a), the low matrix modulus results in fiber
buckling parallel and perpendicular to the beam flexure due to
weak bonding and low resistance to crack propagation during
loading. As the matrix modulus is increased, buckling is isolated
to the in-plane surface as in Figure 3 (b). Here, the increased
modulus results in stronger matrix-fiber interfacial bond that
more readily supports the material and prevents continued crack
propagation. Lastly, the failure mode transitions to delamination
splitting microbuckling in Figure 3 (c) associated with the high
matrix modulus, again, a result of the correspondingly high
interfacial bonding that prevents global crack propagation
between ply layers. Instead, this mechanism consists of a
relatively gradual accumulation of localized surface
delamination followed by buckling of fibre bundles. Here, the
bending strength is dominated by the composite shear strength
and the fibre/matrix adhesion [6].
Overall, composite system properties can be estimated using the
rule of mixtures, as shown in Equations 2, 3 and 4 [5]. These
equations describe how the constituent materials combine to
define the system parameters and is a sufficient mathematical
model for this application.
𝜎𝜎𝑐𝑐 = 𝜎𝜎𝑓𝑓 𝑉𝑉𝑓𝑓 + 𝜎𝜎𝑚𝑚 𝑉𝑉𝑚𝑚 (2)
(a) (b)
(a) (b) (c)

Stephen Roper
𝐸𝐸𝑐𝑐 = 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓 + 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚 (3)
𝜌𝜌𝑐𝑐 = 𝜌𝜌𝑓𝑓 𝑉𝑉𝑓𝑓 + 𝜌𝜌𝑚𝑚 𝑉𝑉𝑚𝑚 (4)
In designing the QSET Loop-Wheel, these material
considerations highlight the importance of fiber/matrix
interfacial compatibility and the system’s Young’s modulus.
These results suggest the application of a medium-strength
Young’s modulus composite for improved bending behaviour,
while limiting the failure mode to in-plane microbuckling; this
failure mode can be offset with the addition of cross-plies as
previously mentioned. Also supported by previous case studies,
this suggests glass fiber and epoxy matrix constituents will be
suitable for the QSET spring application [3] [4].
2.2 Spring Geometry
While microstructural geometry was considered in the previous
section, the macroscopic spring geometry can also be tailored to
create the desired mechanical responses. These characteristics
include energy absorption and release mechanisms, spring rate
and resistance to permanent deformation. As with the laminate
design and material properties, this geometric influence also
extends to the system failure modes [3] [4].
First, composite tubes were analyzed to understand their flexural
performance under compressive loads including crush behavior
and deformation failure characteristics for crashworthiness
applications. This study was conducted experimentally using
woven glass/epoxy elliptical tubes with elliptical ratios ranging
from 0.5 − 2 [9]. The results indicated that for small elliptically
ratios, lots of deformation was seen in earlier collapse, with
crazing and cracking in the polymer matrix and elastic hinge
formation [9]. The resulting load-displacement diagram is shown
in Figure 4, which shows a smooth response until the initial onset
of failure, and the remaining staggered deformation profile as the
structure was continually strained (𝑎𝑎/𝑏𝑏 = 0.5, 0.57, 0.67).
Next, load-deformation of a second group was identified (𝑎𝑎/𝑏𝑏 =
0.8, 1, 1.25), which have fewer peaks and showed no sudden
gradual drop in load. Tubes in this set experienced flattening in
the pre-collapse stage. At this point it was also suggested that
collapse initiation was given by the ellipticity ratio and as it
increases, the initial crack formation decreases [9]. Finally, a
third set (𝑎𝑎/𝑏𝑏 = 1.5, 1.75, 2) was tested and showed energy
absorbed in the pre-collapse was smaller than the post-collapse.
Here, the top and bottom surfaces bend inward and dimple,
developing fracture lines on the innermost surface of the tube
wall. The basic energy dissipation mechanism during initial
collapse was identified as bending about the shell generators,
producing flat surfaces at top and bottom and elastic hinges and
in the post-collapse phase the formation of fracture lines act as
the main energy dissipation mechanism [9].
In general, the experimental results reveal that elliptical tubes
exhibit larger collapse stokes and increased specific energy
dissipation in comparison to circular geometries (𝑎𝑎/𝑏𝑏 = 1). In
this experiment, elliptical tubes reached a maximum stroke of
94% from the original diameter. At 𝑎𝑎/𝑏𝑏 = 0.67, the tube
showed excellent structural integrity with an initial failure load
of 1100N (see Figure 4). This analysis also revealed, that
deviation form circular cross section results in better energy
absorption capability (See Figure 5). This is a significant
deviation from the initial QSET prototype, which used a circular
geometry (𝑎𝑎/𝑏𝑏 = 1); the design now uses an ellipticity ratio of
(𝑎𝑎/𝑏𝑏 = 0.82).
Figure 4: Composite tube under compression, linking energy dissipation
mechanisms to load-displacement characteristics (𝑎𝑎/𝑏𝑏 = 0.67) [9].
Figure 5: Effect of ellipticity ratio on energy absorption characteristics [9].

Stephen Roper
This research also examined the failure mechanisms during the
crushing process. The observed micro energy dissipation
sequence can be summarized by Equation 5 with failure mode
micrographs available in Figure 6 [9].
𝑊𝑊𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑊𝑊𝑚𝑚𝑚𝑚 + 𝑊𝑊𝑓𝑓𝑓𝑓 + 𝑊𝑊𝑏𝑏𝑏𝑏 + 𝑊𝑊𝑙𝑙 𝑙𝑙 (5)
𝑊𝑊𝑚𝑚𝑚𝑚: Energy required to crack/craze the matrix and increase
crack growth.*
𝑊𝑊𝑓𝑓𝑓𝑓: Energy to debond woven fabric from matrix.
𝑊𝑊𝑏𝑏𝑏𝑏: Break and crush fibers.
𝑊𝑊𝑙𝑙 𝑙𝑙: Local delamination.
* In polymer matrix systems, cracks are often initiated at locations
where several fibers debond from the matrix [9].
From the experimental results, the initial energy absorbed in the
system is dissipated to crack the matrix, starting at the top of the
tube. As load and strain is further increased the density and
extent of matrix cracks progress, leading to interfacial debonding
and further leaving fibers unsupported and more compliant. In
turn, this leads to fiber breaking and finallyto local delamination.
The contribution of these energy dissipating micro mechanisms
is significantly influenced by the tube crush strain; as strain
increases, so does the contribution of the micro mechanism
leading to degraded properties in the crush zone [9].
Figure 6: Failure modes in composite tubes, microstructural analysis. (a) Matrix
cracking; (b) Fibre debonding from the matrix, (c) Fibre breakage, (d) local
delamination. Magnification of 100μm. [9].
It should also be note that micro mechanical failure by shear and
microbuckling were unseen in this case study. Under the tested
geometry and material properties, these alternate modes were
replaced instead by extensive matrix crack propagation and
interfacial debonding, leaving the fibers unsupported for
microbuckling or shear failure to occur. Furthermore, the
interweaving fiber architecture prevented global buckling as well
as gross delamination of tube wall sides. The cross-plies reduced
interlaminar crack propagation between layers and prevented
splitting along fracture lines, where interweaving fibers
supported each other to carry the load [9].
Macro mechanical failure modes were also identified as energy
dissipation mechanisms, and divided into two categories: with
𝑎𝑎/𝑏𝑏 < 0.8, 1, 1.25 and 𝑎𝑎/𝑏𝑏 > 1.5. These mechanisms are
summarized by Equation 6 and Equation 7, respectively. In all
cases, the two macro dissipation categories are functions of the
ellipse ratio. For example, when 𝑎𝑎/𝑏𝑏 is sufficiently small the
developed strain does not exceed that for forming an elastic
hinge on the bottom surface or tube wall fracture. Instead, when
𝑎𝑎/𝑏𝑏 is large, enough strain is developed to form elastic hinges at
the bottom and even fracture the outermost surface of the wall.
𝑊𝑊𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑜𝑜1
= 𝑊𝑊𝑓𝑓𝑓𝑓 + 𝑊𝑊𝑐𝑐𝑐𝑐 + 𝑊𝑊𝑓𝑓 (6)
𝑊𝑊𝑓𝑓𝑓𝑓: Energy dissipated in flexure.
𝑊𝑊𝑐𝑐𝑐𝑐: Energy dissipation in circumferential deformation.
𝑊𝑊𝑓𝑓: Energy dissipated in forming fracture lines: increases
as fracture lines increase.
𝑊𝑊𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑜𝑜2
= 𝑊𝑊𝑓𝑓𝑓𝑓 + 𝑊𝑊𝑚𝑚 + 𝑊𝑊𝑓𝑓ℎ + 𝑊𝑊𝑓𝑓𝑓𝑓 + 𝑊𝑊𝑓𝑓 + 𝑊𝑊𝑓𝑓𝑓𝑓
(7)
𝑊𝑊𝑓𝑓𝑓𝑓: Energy dissipated in flattening deformation
(negligible).
𝑊𝑊𝑚𝑚: Energy absorbed during column formation (left and
right hand side of tube wall). *
𝑊𝑊𝑓𝑓ℎ: Energy dissipated during formation of elastic hinges
(significant). **
𝑊𝑊𝑓𝑓𝑓𝑓:
Energy dissipated during flexure strongly influenced by
ratio, and localized at the hinges.
𝑊𝑊𝑓𝑓: Energy dissipated during fracture line formation.
𝑊𝑊𝑓𝑓𝑓𝑓: Energy associated with frictional forces induced after
the formation of fracture lines. ***
* Increases as ratio increases since structural materials are generally
more efficient in tension rather than in flexure.
** Increase tube energy absorption by encouraging the formation of
elastic hinges and thus mitigating more destructive alternate failure
mechanisms.
*** Due to sliding of the outermost surface against each other and platens.
This analysis revealed practical consideration for the QSET
design. First, a considerable increase in carrying capacity and the
energy absorption capability can be achieved by introducing an
elliptical cross sectional geometry compared to a circular one [9].
The specific spring characteristics can be further controlled by
the ellipticity ratio, where adjustments in the major and minor
dimensions can improve the level of energy absorption of the
laterally compressed tubes [9]. Lastly, the characteristic failure
modes and onset of semi-permanent deformation was found to
(a) (b)
(c) (d)

Stephen Roper
depend on constituent material interactions and ellipticity ratio.
Choosing a matrix with a large strain to failure will help avoid
the onset of microcracks, and incorporating a design with a large
ellipticity ratio can eliminate the appearance of elastic hinges [9].
The addition of 0/90 cross plies can further help avoid these
failure modes, with intertwining fibers reducing propagation
between ply layers.
A second study modified the classical elliptical design to include
flat contact surfaces for facilitating practical use and fixture
applications (Figure 7). This investigation focused on the
mechanical properties of eighteen different samples linking the
critical geometric properties to load and displacement
performance, and comparing physical testing and finite element
results. For this analysis, a 0/90 plain weave E-glass/epoxy
woven composite with 5-ply, 7-ply, and 9-ply thicknesses were
used [10].
Figure 7: Modified composite spring geometry with parallel flat contact surfaces
[10].
For this experiment, the load-displacement and strain
distribution of thin shell springs were determined, specifically
examining the effect of spring radii and thickness (22: 7 <
𝑅𝑅: 𝑡𝑡 < 87: 7). This analysis was conducted considering two
loading cases; surface loading applied to the top and bottom
surfaces and line-loading on the center of the flat surface.
From this analysis a linear load-deflection relationships was
observed for up to 2mm. Once deflection exceeded this amount
the response transitioned to a weak non-linear relationship [10].
Like with the tubular springs, geometric properties were also
observed to have a significant impact on the load-deflection
performance of the structure. For example, as thickness
increased the ultimate load of the specimen increased. Contrarily,
as spring radius increased ultimate load decreased with a more
sensitive response. Figure 8 shows the load-displacement curves
for both loading conditions, and highlights the onset of failure
(marked “cracking sound”) [10].
Figure 8: Load-displacement characteristics of the modified spring geometry.
This also shows the suitability for FE analysis in design applications, up to the
onset of failure which involves various complex mechanisms [10].
Figure 9: Spring thickness-to-radius of curvature compared to the ultimate load
[10].
To further understand the load-carrying capacity of the springs
and the effect of geometry correlation curves were plotted using
normalized loading and geometrical data (Figure 9). This data
suggests an appropriate way to predict ultimate load knowing the
thickness, radius and stiffness characteristics. One of the most
significant findings indicated that when the radius-to-thickness
ratio was small (Large 𝑅𝑅 and small 𝑡𝑡), failure was not readily
induced (ultimate load not easily achieved).
This study revealed various practical aspects of spring
performance and design, highlighting the need for large
deflection analysis; when designing the QSET Loop-Wheel FE
analysis was applied. One of the other significant outcomes were
the correlation curves provide estimates of the ultimate load of a
spring with known thickness, radius, stiffness. To obtain the
desired spring characteristics and help offset failure modes a
radius-to-thickness ratio of 62:5 was used in the final design.
2.3 Composite Failure Modes
After developing an understanding of the interactions and
influence of laminate design, material properties, and geometry
on load-deformation behaviour and the onset of failure a more
detailed investigation into the microstructure during flexure was
desired. This analysis focuses on the failure mechanisms found

Stephen Roper
throughout a structural component in flexure, specifically on the
maximum tensile, compressive, and shear regions [11]. While
these studies were conducted in four-point bending the can be
related to deformation characteristics of an elliptical composite
spring.
The onset of each failure mode can be summarized by Figure 10,
which shows the expected mechanisms as the laminate degrades
from micro energy dissipation mechanisms (cracking, spalling).
Figure 10: Composite failure mode trends, related to interfacial strength [11].
2.3.1 Tension
In elliptical composite springs maximum tension is experienced
on the outer surface, stretching the constituent materials. Upon
initial straining, fiber ridges appear near the surface as they bulge
outward prior to matrix cracking [11]. As the fiber/matrix
interface is stretched, the interface begins to breakdown as
shown in Figure 11.
As the spring is strained further microcracks begin to form
perpendicular to the direction of stress as in Figure 12. This
causes the matrix to fail in brittle fracture and further increase
the flaw size and intensity [11].
As the flaw size increases cracks elongate and intersect with
neighboring fibers at the surface. Local weaknesses and fiber
defects can cause the matrix microcracks to propagate and split
the fibers causing fiber/matrix interfacial failure (Figure 13)
[11]. Other cracks can continue to propagate along the
fiber/matrix interfacial bonding zones, longitudinally and
transversely until they converge [11]. As fiber and matrix
continue to fracture stress concentrations appear in the remaining
fibers until the sequence breaks the composite as a whole.
Figure 11: Initial fiber ridging on the tensile surface of the spring [11].
Figure 12: Microcrack formation at the tensile surface of the spring [11].
Figure 13: Fiber fracture and debonding from the matrix on the tensile surface
as the interface continues to degrade [11].

Stephen Roper
2.3.2 Compression
As an elliptical spring is compressed the inner-most surface
experiences compressive forces. Like with the tensile surface,
early stages of deformation involve fiber ridging and bulging at
the surface (Figure 14). However, as the load is increased matrix
spalling occurs, which effectively crumbles the matrix over the
ridged fibers instead of transverse matrix cracking in tension
(Figure 15).
As the matrix spalling increases the breakdown between fiber
and matrix constituents increases and presents the onset of
microbuckling at the region of maximum displacement in the
through thickness direction (Figure 16). This causes permanent
sliding between the buckled and non-buckled plies. It is evident
that microbuckling is closely related to both the interfacial
tensile and interfacial shear strength; a strong interface is more
likely to be able to prevent microbuckling from occurring, as
with the addition of cross plies [11].
Figure 14: Initial fiber ridging on the compressive surface of the spring [11].
Figure 15: Matrix spalling and degradation on the inner compressive surface of
the spring [11].
Figure 16: Microbuckling on the inner compressive surface at a region of
maximum displacement (cross sectional view) [11].
2.3.3 Shear
From beam theory, failure modes from shear stresses are also
expected in the composite springs at the mid-plane (area of
maximum shear stress) [12]. In this case, shear cracks propagate
parallel to the fiber/matrix interface, along the weakest portion
of the material.
Figure 17: Failure mechanism in the shear failure mode.
This analysis revealed that stronger interface can offset the shear
failure mode. This can be achieved with a high density of
residual matrix particles bonding to the fibers in an evenly
dispersed laminate [11]. This is discussed in more detail in
Section 3, next.

Stephen Roper
3 MANUFACTURING
Another microstructural consideration for the final spring design
is the manufacturing process and resulting defects that lead to
detrimental mechanical properties. The two primary
considerations are: void content and fiber/fabric alignment.
Voids are one of the most common manufacturing variables for
fiber/epoxy laminates. While specialized techniques and
procedures can be used to fabricate void-free composites, these
practices are often not economically feasible [13]; this extends
to the limited resources directly available to QSET. One study
examined the effect of specific void content on over thirty
different laminate samples made from unidirectional carbon
fiber, resin matrix systems. These results found that overall, an
increase in void content by 11% resulted in a reduction in
interlaminar shear strength (ILSS) up to 41% [13]. There is also
a direct correlation between void content and void dispersion
throughout the microstructure, with low amounts apparently
segregated to specific portions of the sample and larger void
volume fractions resulting in a more even distribution [13]. This
can affect the onset of failure, with voids located near high stress
areas (neutral axis) resulting in weaker interlaminar shear
strength to resist against crack propagation. The effects of voids
on interlaminar shear strength can be described by Equation 8,
which represents the ILSS compared to a void-free sample [13].
𝐼𝐼𝐼𝐼𝐼𝐼𝑆𝑆𝑟𝑟 = 1 − �
4𝑉𝑉𝑣𝑣
3.14�1 − 𝑉𝑉𝑓𝑓�
�
0.5
(8)
𝐼𝐼𝐼𝐼𝐼𝐼𝑆𝑆𝑟𝑟: 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 of the composite with voids relative to an
equivalent void-free composite
𝑉𝑉𝑓𝑓: Volume fraction of the fiber.
𝑉𝑉𝑣𝑣: Volume fraction of the voids.
In general, as void content increases the ILSS decreases and
makes the sample more susceptible to failure in compression. In
the case of the QSET composite spring, this suggests greater
sensitivity to microbuckling and delamination failure modes,
compared to the fiber splitting on the tensile surface.
Fiber alignment is another consideration during composite
manufacture and includes fiber waviness and wrinkles. First,
fiber waviness is characterized by fabrics that are not sufficiently
stretched during the initial fabric layup [14]. That is, the fibers
are not aligned parallel to each other or their common intended
reference. Wrinkles, or out-of-plane waviness, are also common
fabrication faults where the fabric is bunched against the
preformed component die [14]. See Figure 22. In both cases, the
reinforcing fiber phase is not completely utilized upon loading,
requiring the weaker matrix to sustain the stress in these areas.
As a result, matrix cracking and spalling is more likely to occur
until the fibers self-align. At this point the interlaminar bond and
fiber surfaces will be damaged and result in further crack
propagation until fracture of both constituent phases occurs.
Figure 18: Manufacturing induced defects: (a) fabric waviness (b) fabric kinks
(out-of-plane waviness)[14].
These defects are more common in hand-layup manufacturing
process such as vacuum bag molding; this is the process QSET
will use to form the final composite spring. Attention to the
fabric layup should be taken to avoid the in-plane and out-of-
plane waviness.
4 DESIGN AND FE MODELING
4.1 Design
The QSET Loop-Wheel spring design has evolved considerably
from the initial concept into the proposed version from this
investigation. The first prototype developed by the team utilized
a circular cross section, however this was transitioned to a semi-
elliptical version following research in automotive leaf spring
design. The final proposed solution incorporates a continuous
elliptical cross section with parallel flat platens for easy fixture
to the wheel components, as suggested by previous research. The
geometry uses an ellipticity ratio of 0.82 for improved energy
absorbing properties and incorporates a sufficiently small radius-
to-thickness ratio of 65:3 to help offset failure modes.
Figure 19: Design progression: (a) semi-elliptical spring design (b) final
continuous elliptical spring with flat platens.
For this design S-Glass unidirectional fiber fabric and an epoxy
matrix were selected as the constituent materials. This follows
current composite spring trends and is expected to provide the
system with suitable mechanical properties without being over
designed. To approximate the S-Glass/epoxy plies for the FE
analysis a known material was selected as shown in Table 1. The
material properties for this system have been experimentally
tested in a resin pre-impregnated form and are found in Table 2.
(a) (b)

Stephen Roper
Table 1: S-Glass/epoxy composite form [8].
Material
S2-449 17k/SP 381 unidirectional tape (E-
Glass/Epoxy)
Fiber Owens Corning S2-449, no twist, no surface
Matrix 3M SP 381
Table 2: Mechanical properties for high-temperature application resins [8].
Units Nominal
Ply Thickness mm 0.3
𝝆𝝆 kg/m3
1910
𝑬𝑬𝟏𝟏 GPa 47.8
𝑬𝑬𝟐𝟐 GPa 12.3
𝑮𝑮𝟏𝟏𝟏𝟏 GPa 0.0998
𝝂𝝂𝟏𝟏𝟏𝟏 - 0.318
𝑿𝑿 MPa 1758
𝑿𝑿′ MPa 1185
𝒀𝒀 MPa 60
𝒀𝒀′ MPa 45
𝑺𝑺𝟏𝟏𝟏𝟏 MPa 136
4.2 FE Model
4.2.1 Model Setup
A finite element model of the spring was created in HyperWorks,
using PSHELL elements and the MAT8 material cards; this
allowed for sufficient definition of the composite material
properties. The plie orientations were applied and then stacked
according to the designs specific in Table 3. These designs were
based on the previous research to provide sufficient load and
displacement characteristics, while introducing cross plies (90°
and ±45°) to offset delamination and microbuckling failure
modes.
Table 3: Laminate design investigation.
Design Laminate Stack
A [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
B [90, 0, 0, 0, 0, 0, 0, 0, 0, 90]
C [+45, -45, 0, 0, 0, 0, 0, 0,-45, +45]
D [+45, -45, 90, 0, 0, 0, 0, 90,-45, +45]
E [+45, -45, 0, 0, 90, 90, 0, 0,-45, +45]
These models were tested under a worst case loading condition,
assuming the entire rover weight (125lbs) was placed on a single
wheel. With three springs per wheel, and accounting for a safety
factor of 1.5, the applied load on each spring is 280N.
Figure 20: Loading condition for FE analysis.
4.2.2 Results
The results from the FE analysis indicated that Design E is the
most suitable for the spring application. It showed a good
balance between load and displacement characteristics while the
introduction of cross-plies would help offset the failure modes
seen earlier, namely delamination and microbuckling. These
results are summarized in Figure 20.
Figure 21: Spring laminate design comparison.
The results from Design E can be shown in Figure 21, which
show the expected deformation behaviour. Here, the load is
being successfully transferred to the outer spring sections and
compressing uniformly for a maximum deflection of 14.5mm.
Figure 22: Maximum displacement and deformation behaviour of Design E.
5 CONCLUSIONS
After completing an analysis of composite spring geometry,
constituent materials and deformation characteristics final
conclusions have been drawn to propose a suitable spring design.
Recommendations have also been provided for future work to
expand on this analysis:
1. Failure modes that must be accounted in spring design
appear in tension, compression and shear surfaces. These
are: fiber ridging, matrix microcracking and crazing, crack
propagation and intensification parallel and perpendicular to
the fiber-matrix interface, delamination, microbuckling,
fiber-matrix splitting.
(a) Due to the appearance of voids from fabrication, the
spring is expected to be more sensitive in
compression.
2. Adjusting overall spring geometry has a significant effect on
the energy absorbing characteristics of composite springs
and is most impacted by ellipticity ratio and radius-to-
thickness ratio.
0
5
10
15
20
A B C D E
MaximumDisplacement
[mm]
Design
Spring Design Comparison
𝑃𝑃 =
𝐹𝐹
𝑎𝑎
=
280
0.005
= 56,000
N
m2
C𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎𝑎𝑎 𝐷𝐷𝐷𝐷𝐷𝐷

Stephen Roper
(a) The final design incorporates an ellipticity ratio of
0.82, allowing for improved energy absorbing
characteristics compared to a circular cross section
within the Loop-Wheel geometrical constraints.
(b) The final design incorporates a radius-to-thickness
ratio of 65:3 to help offset delamination and
microbuckling failure modes.
3. Adjusting microstructure (ply style, orientation and
thickness) of the laminate affects the mechanical properties
and can be designed to offset failure modes.
(a) The final design utilizes 0° fibers oriented in the
longitudinal direction (circumferential) as the main
support structure for the spring.
(b) The final design incorporates both 90° and ±45°
cross plies to prevent crack propagation and
delamination throughout the laminate.
(c) The ten layer lamina stack in the final design offers
sufficient load-deflection characteristics while
maintaining the desired cross-ply, and radius-to-
thickness parameters. The stack is symmetric and
follows Design E:
[+45, -45, 0, 0, 90, 90, 0, 0, -45, +45]
(d) The maximum deflection in the system is
approximately 14.5mm, offering an adequate
compressive stroke to dampen larger loads.
4. Constituent materials have an effect on the flexural
characteristics of the spring, most significantly driven by the
Young’s modulus of the system.
(a) S-Glass and epoxy constituent materials were chosen
due to their similar strain to failures and material
compatibility. This should ensure good interfacial
bond strength with readily sourced and
manufacturable materials. This combination also
offers a medium strength Young’s modulus to
balance between flexural rigidity and less severe
failure modes (in-plane microbuckling against
delamination microsplitting).
5. Additional work should be conducted to better understand
the constituent material interfacial bond, specifically in
regard to fiber coatings and surface treatments. Here,
constituent materials were chosen based on their current
successful application, similar properties (strain to failure),
and combined Young’s modulus.
6. Additional work should be conducted to apply FE failure
theory to the composite model. This could help predict the
onset of individual ply failure, but is limited by its accuracy
in simulating complex mechanisms. See Appendix A for an
initial investigation into orthotropic failure theories.
6 REFERENCES
[1] Beoing, Boeing Commercial Quartley Report, Boeing
Aero, 2006.
[2] E. Mahdi, O. Alkoles, A. Hamouda, B. Sahari, R. Yonus
and G. Goudah, "Light Composite Elliptic Springs for
Vehicle Suspension.," Composite Structures, vol. 75, pp.
24-28, 2006.
[3] H. Al-Qureshi, "Automobile Leaf Springs from Composite
Materials," Materials Processing Technology, vol. 118, pp.
58-61, 2001.
[4] A. R. A. Talib, A. Ali, G. Goudah, N. A. C. Lah and A.
Golestaneh, "Developing a Composite Based Elliptic
Spring for Automotive Applications," Materials and
Design, vol. 31, pp. 475-484, 2010.
[5] G. Haritos, J. Hager, A. Amos and M. Salkind,
"Mesomechanics: The Microstructure-Mechanics
Connection," Solids Structures, vol. 24, no. 11, pp. 1081-
1096, 1988.
[6] F. Chen, S. Bazhenov, A. Hiltner and E. Baer, "Flexural
Failure Mechanisms in Unidirectional Glass Fiber-
Reinforced Thermoplastics," Composites, vol. 25, no. 1,
pp. 11-20, 1994.
[7] E. Madi and A. Hamouda, "An Experimental Investigation
into Mechanical Behavior of Hybrid and Nonhybrid
Composite Semi-Elliptical Springs," Materials and
Design, vol. 52, pp. 504-513, 2013.
[8] P. Tse, S. Reid, K. Lau and W. Wong, "Large Deflections
of Composite Circular Springs with Extended Flat Contact
Surfaces," Composite Structures, vol. 63, pp. 253-260,
2004.
[9] Department of Defense Handbook, "Polymer Matrix
Composites, Material Usage, Design and Analysis (MIL-
HDBK-17-3F)," 2002.
[10] E. Mahdi, O. Alkoles, A. Hamouda and B. Sahari,
"Ellipticity Ratio Effects in the Energy Absorption of
Laterally Crushed Composite Tubes," Advanced
Composite Materials, vol. 15, no. 1, pp. 95-113, 2006.
[11] G. Shih and L. Ebert, "Flexural Failure Mechanisms and
Global Stress Plane for Unidirectional Composites
Subjected to Four-Point Bending Tests," Composites, vol.
17, no. 4, pp. 309-320, 1986.
[12] S. Birger, A. Moshonov and S. Kenig, "Failure
Mechanisms of Graphite-Fabric Epxoy Composites
Subjected to Flexural Loading," Composites, vol. 20, no.
2, pp. 136-144, 1989.
[13] K. J. Bowles and S. Frimpong, "Void Effects on the
Interlaminar Shear Strength of Unidirectional Graphite-
Fiber-Reinforced Composites," Composite Materials, vol.
26, no. 10, pp. 1487-1509, 1992.
[14] J. S. Lightfoot, M. R. Wisnom and K. Potter, "Defects in
Woven Preforms: Formation Mechanisms and the Effects
of Laminate Design and Layup Protocol," Composites,
vol. 51, no. Part A, pp. 99-107, 2013.
[15] G. Sih, A. Skudra and R. Rowlands, "Chapter II: Strength
(Failure) Theories and their Experimental Correlation," in
Failure Mechanics of Composites, Amsterdam, Elsevier
Science Publishers, 1985, pp. 86-97.

Stephen Roper
PAGE INTENTIONALLY LEFT BLANK
S. ROPER, 26/04/2016

Stephen Roper
APPENDIX A: COMPOSITE FAILURE THEORIES IN FE MODELING
To further understand the mechanical properties of laminate
structures orthotropic failure theories were studied to
characterize ply deterioration. The main orthotropic yield
functions to consider for future elliptical spring analysis are
Maximum Strain and Tsai-Wu theories. These are readily
supported by HyperWorks, along with Hill and Hoffman yield
functions, and can be used to predict the failure behaviour of
individual plies.
The Maximum Strain theory provides suitable laminate strength
predictions with respect to applied loads and stresses (in-plane
and bending) and can isolate specific plies to suggest
corresponding failure modes such as debonding and fiber failure.
This criteria is typically used for unsymmetrical laminates and
assumes a linear-elastic response where failure is predicted when
strain reaches its limiting values (determined by uniaxial tensile
experiments) [15]. To apply this criterion lamina elastic
properties (𝐸𝐸1, 𝐸𝐸2, 𝜈𝜈12, 𝐺𝐺12) are required as basic inputs as well
as longitudinal, transverse, and shear strengths in tension and
compression (𝑋𝑋, 𝑌𝑌, 𝑋𝑋′
, 𝑌𝑌′
, 𝑆𝑆12). See Equation A1.
𝐹𝐹 = max��
𝜀𝜀1
𝑋𝑋�
�, �
𝜀𝜀2
𝑌𝑌�
�, �
𝛾𝛾12
𝑌𝑌�
�� (A1)
Like the Maximum Strain criteria, the Tsai-Wu theory assumes
plane stress with a linear elastic lamina response and is preferred
for predicting the onset of laminate failure, but not the specific
mode (transverse, shear). This yield criteria is invariant under
coordinate system rotation, making it superior to alternatives like
the Hoffman criteria, and provides independent interactions
among stress components. The same material properties used for
the Maximum Strain theory are required here, however the
ultimate strength values are insufficient for determining
coefficients such as the stress interaction term 𝐹𝐹12 [15]. The Tsai-
Wu failure theory is presented in Equation A2.
𝐹𝐹1 𝜎𝜎1 + 𝐹𝐹2 𝜎𝜎2 + 𝐹𝐹6 𝜎𝜎6 + 𝐹𝐹11 𝜎𝜎1
2
+ 𝐹𝐹22 𝜎𝜎2
2
…
+ 2𝐹𝐹12 𝜎𝜎1 𝜎𝜎2 + 𝐹𝐹66 𝜎𝜎6
2
= 1
(A2)
In HyperWorks, these failure criteria can be used to generate
failure index contour plots (Equation A3), to indicate the location
and magnitude of high stress regions. The output can also be
adjusted to include a composite strength ratio, which indicates
the safety factor distribution throughout the structure (Equation
A4).
𝐹𝐹𝐹𝐹 > 1, 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐹𝐹𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 (A3)
𝑆𝑆𝑆𝑆 > 1, 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 (A4)
Content in Appendix A adapted from: S. Roper, “Finite Element Analysis and
Design Optimization of an eBike Structure Using Carbon Fiber Composites”
MECH461: Undergraduate Research Project, 2016.

Stephen Roper
APPENDIX B: PROPOSED SPRING GEOMETRY

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