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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Automotive Series
- Sprache: Englisch
A design reference for engineers developing composite components for automotive chassis, suspension, and drivetrain applications This book provides a theoretical background for the development of elements of car suspensions. It begins with a description of the elastic-kinematics of the vehicle and closed form solutions for the vertical and lateral dynamics. It evaluates the vertical, lateral, and roll stiffness of the vehicle, and explains the necessity of the modelling of the vehicle stiffness. The composite materials for the suspension and powertrain design are discussed and their mechanical properties are provided. The book also looks at the basic principles for the design optimization using composite materials and mass reduction principles. Additionally, references and conclusions are presented in each chapter. Design and Analysis of Composite Structures for Automotive Applications: Chassis and Drivetrain offers complete coverage of chassis components made of composite materials and covers elastokinematics and component compliances of vehicles. It looks at parts made of composite materials such as stabilizer bars, wheels, half-axes, springs, and semi-trail axles. The book also provides information on leaf spring assembly for motor vehicles and motor vehicle springs comprising composite materials. * Covers the basic principles for the design optimization using composite materials and mass reduction principles * Evaluates the vertical, lateral, and roll stiffness of the vehicle, and explains the modelling of the vehicle stiffness * Discusses the composite materials for the suspension and powertrain design * Features closed form solutions of problems for car dynamics explained in details and illustrated pictorially Design and Analysis of Composite Structures for Automotive Applications: Chassis and Drivetrain is recommended primarily for engineers dealing with suspension design and development, and those who graduated from automotive or mechanical engineering courses in technical high school, or in other higher engineering schools.
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Table of Contents
Cover
Foreword
Series Preface
List of Symbols and Abbreviations
Abbreviations
Introduction
Composites in Automotive Chassis and Drivetrain
Physical Properties of Composite Materials
Structure of the Book
Target Audience of the Book
References
About the Companion Website
1 Elastic Anisotropic Behavior of Composite Materials
1.1 Anisotropic Elasticity of Composite Materials
1.2 Unidirectional Fiber Bundle
1.3 Rotational Transformations of Material Laws, Stress and Strain
1.4 Elasticity Matrices for Laminated Plates
1.5 Coupling Effects of Anisotropic Laminates
1.6 Conclusions
References
2 Phenomenological Failure Criteria of Composites
2.1 Phenomenological Failure Criteria
2.2 Differentiating Criteria
2.3 Physically Based Failure Criteria
2.4 Rotational Transformation of Anisotropic Failure Criteria
2.5 Conclusions
References
3 Micromechanical Failure Criteria of Composites
3.1 Pullout of Fibers from the Elastic‐Plastic Matrix
3.2 Crack Bridging in Elastic‐Plastic Unidirectional Composites
3.3 Debonding of Fibers in Unidirectional Composites
3.4 Conclusions
References
4 Optimization Principles for Structural Elements Made of Composites
4.1 Stiffness Optimization of Anisotropic Structural Elements
4.2 Optimization of Strength and Loading Capacity of Anisotropic Elements
4.3 Optimization of Accumulated Elastic Energy in Flexible Anisotropic Elements
4.4 Optimal Anisotropy in a Twisted Rod
4.5 Optimal Anisotropy of Bending Console
4.6 Optimization of Plates in Bending
4.7 Conclusions
References
5 Optimization of Composite Driveshaft
5.1 Torsion of Anisotropic Shafts With Solid Cross‐Sections
5.2 Thin‐Walled Anisotropic Driveshaft with Closed Profile
5.3 Deformation of a Composite Thin‐Walled Rod
5.4 Buckling of Composite Driveshafts Under a Twist Moment
5.5 Patents for Composite Driveshafts
5.6 Conclusions
References
6 Dynamics of a Vehicle with Rigid Structural Elements of Chassis
6.1 Classification of Wheel Suspensions
6.2 Fundamental Models in Vehicle Dynamics
6.3 Forces Between Tires and Road
6.4 Dynamic Equations of a Single‐Track Model
6.5 Conclusions
References
7 Dynamics of a Vehicle With Flexible, Anisotropic Structural Elements of Chassis
7.1 Effects of Body and Chassis Elasticity on Vehicle Dynamics
7.2 Self‐Steering Behavior of a Vehicle With Coupling of Bending and Torsion
7.3 Steady Cornering of a Flexible Vehicle
7.4 Estimation of Coupling Constant for a Twist Member
7.5 Design of the Countersteering Twist‐Beam Axle
7.6 Patents on Twist‐Beam Axles
7.7 Conclusions
References
8 Design and Optimization of Composite Springs
8.1 Design and Optimization of Anisotropic Helical Springs
8.2 Conical Springs Made of Composite Material
8.3 Alternative Concepts for Chassis Springs Made of Composites
8.4 Conclusions
References
9 Equivalent Beams of Helical Anisotropic Springs
9.1 Helical Compression Springs Made of Composite Materials
9.2 Transverse Vibrations of a Composite Spring
9.3 Side Buckling of a Helical Composite Spring
9.4 Conclusions
References
10 Composite Leaf Springs
10.1 Longitudinally Mounted Leaf Springs for Solid Axles
10.2 Leaf‐Tension Springs
10.3 Transversally Mounted Leaf Springs
10.4 Conclusions
References
11 Meander‐Shaped Springs
11.1 Meander‐Shaped Compression Springs for Automotive Suspensions
11.2 Multiarc‐Profiled Spring Under Axial Compressive Load
11.3 Sinusoidal Spring Under Compressive Axial Load
11.4 Bending Stiffness of Meander Spring With a Constant Cross‐Section
11.5 Stability of Corrugated Springs
11.6 Patents for Chassis Springs Made of Composites in Meandering Form
11.7 Conclusions
References
12 Hereditary Mechanics of Composite Springs and Driveshafts
12.1 Elements of Hereditary Mechanics of Composite Materials
12.2 Creep and Relaxation of Twisted Composite Shafts
12.3 Creep and Relaxation of Composite Helical Coiled Springs
12.4 Creep and Relaxation of Composite Springs in a State of Pure Bending
12.5 Conclusions
References
Appendix A: Mechanical Properties of Composites
A.1 Fibers
A.2 Physical Properties of Resin
A.3 Laminates
References
Appendix B: Anisotropic Elasticity
B.1 Elastic Orthotropic Body
B.2 Distortion Energy and Supplementary Energy
B.3 Plane Elasticity Problems
B.4 Generalized Airy Stress Function
Appendix C: Integral Transforms in Elasticity
C.1 One‐Dimensional Integral Transform
C.2 Two‐Dimensional Fourier Transform
C.3 Potential Functions for Plane Elasticity Problems
C.4 Rotationally Symmetric, Spatial Elasticity Problems
C.5 Application of the Fourier Transformation to Plane Elasticity Problems
C.6 Application of the Hankel Transformation to Spatial, Rotation‐Symmetric Elasticity Problems
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Coefficients of Voigt's and Kelvin's matrices for orthotropic material...
Table 1.2 Effective modules of unidirectional composite material (Schürmann 2007...
Table 1.3 Input values for calculation of effective modules.
Table 1.4 Elastic constants and densities of matrix and fibers of UD fiberglass.
Chapter 2
Table 2.1 Overview of strength criteria for fiber‐plastic composites.
Table 2.2 Coefficients of the matrix and tensor Mises–Hill criterion.
Table 2.3 Eigenvalues of the matrix and tensor Mises–Hill criterion.
Table 2.4 Eigenvalues of the matrix for the pressure‐sensitive Mises–Hill crite...
Table 2.5 Material parameters for failure criteria (Vasilev et al. 1990).
Table 2.6 Coefficients of quadratic form of the Hashin strength criterion in a g...
Table 2.7 Coefficients of quadratic form of the Hashin strength criterion in a p...
Table 2.8 Coefficients of quadratic form of the Hashin strength criterion in cas...
Table 2.9 Coefficients of the pressure‐sensitive Mises–Hill criterion in the inc...
Chapter 3
Table 3.1 Coefficients of Eqs. ( 3.47 ) and ( 3.48 ).
Table 3.2 Properties of fiber and matrix for calculations.
Table 3.3 Expressions for integral
χ
n
(
t
)
and solutions for coefficients
C
n
.
Table 3.4 Kernel of the integral equation for elastic cylinder, Eq. ( 3.145 ).
Table 3.5 Kernel of the integral equation for elastic cavity, Eq. ( 3.147 ).
Table 3.6 Kernel of the integral equation for contact problem of elastic cylinde...
Table 3.7 Material data for debonding problem (Barbero 1999 ).
Chapter 5
Table 5.1 Areas and area moments for solid triangular and circular cross‐section...
Table 5.2 Areas and area moments for hollow triangular and circular cross‐sectio...
Chapter 6
Table 6.1 Angle definitions in vehicle dynamics.
Table 6.2 Angle definitions in geometry of chassis.
Table 6.3 Components of forces and moments.
Table 6.4 Under‐, over‐ or neutral‐driving vehicle.
Chapter 8
Table 8.1 Spring rates and masses of the linear springs with a non‐circular wire...
Table 8.3 Stiffness of wires with different cross‐sections of wire.
Table 8.4 Section modules of wires with different cross‐section.
Chapter 9
Table 9.1 Effective stiffnesses for shear, bending and compression and mass per ...
Table 9.2 Conditions at the ends of the spring in terms of shear force, moment a...
Table 9.3 Conditions at the ends of the spring for different loading.
Chapter 10
Table 10.1 Comparison of different concepts for leaf springs (Kobelev et al. 201...
Chapter 11
Table 11.1 Effective spring constants of meander and coil springs for bending an...
Table 11.2 Design formulas for axial and bending stiffness of multiarc and sinus...
Table 11.3 Effective axial stiffness and spring rates of multiarc and sinusoidal...
Table 11.4 Dimensionless functions for multiarc and sinusoidal meander spring wi...
List of Illustrations
Chapter 1
Figure 1.1 Coordinate system and elastic symmetry.
Figure 1.2 Coordinate system associated with fiber direction and rotated coordi...
Figure 1.3 (a) Circumferentially asymmetric stiffness configuration (CAS), (b) ...
Chapter 2
Figure 2.1 The surface of the safety factors for the Tsai–Wu criterion (
α = 1,
...
Figure 2.2 The surface of the safety factors for the Goldenblat–Kopnov criterio...
Figure 2.3 Transformation of tensor‐polynomial failure criteria for a unidirect...
Figure 2.4Figure 2.4 Transformation of tensor‐polynomial failure criteria for a...
Figure 2.5 Transformation of tensor‐polynomial failure criteria for a unidirect...
Chapter 3
Figure 3.1 Types of failure for fiber‐reinforced composite materials.
Figure 3.2 Common types of fracture mechanism of fiber‐reinforced composite mat...
Figure 3.3 Pullout of fibers and rupture surfaces of fibers and matrix on the p...
Figure 3.4 Zones along the pullout fibers. (a) Pulling the fibers from the elas...
Figure 3.5 Bridging of crack surfaces by fibers (a) and by matrix (b).
Figure 3.6 Dependence of the average stress upon the displacement of the matrix...
Figure 3.7 Crack in the unidirectional material.
Figure 3.8 Dependence of the stress to unlimited break in fibers as function of...
Figure 3.9 Dependence of the stress to unlimited break in matrix as function of...
Figure 3.10 Dependence of the stress to unlimited break in fibers and matrix as...
Figure 3.11 Dependence of the stress to unlimited break in fibers and matrix as...
Figure 3.12 Crack section and zone structure.
Figure 3.13 Zones at penny‐shaped crack.
Figure 3.14 Stress intensity factor
K
I
as the function of
.
Figure 3.15 Plane crack problem.
Figure 3.16 Elastic‐plastic pullout of the fiber from the matrix (a) and the sp...
Figure 3.17 Fatigue failure of unidirectional fiberglass‐epoxy composite. Visib...
Figure 3.18 Fiber‐matrix debonding model. (a) Undeformed stress state, perfect ...
Figure 3.19 Fiber‐matrix debonding model. (C) Deformed stress state, perfect ad...
Figure 3.20 Fiber‐matrix debonding model. (A) Undeformed stress state, perfect ...
Figure 3.21 Exact and approximated kernels
K
c
(
η
),
k
c
(
η
)
of the integr...
Figure 3.22 Relation of exact to the approximate kernel
K
c
(
η
)/
k
c
(
η
)
.
Figure 3.23 Normalized solution
g
1
(
η
)/
g
1
(0)
( 3.159 ) for the dimensionle...
Figure 3.24 Right side of the equation
f
(
η
)
for different dimensionless le...
Figure 3.25 The coefficient
c
g
(
a
)/ exp(
a
/2)
as a function of debonding le...
Figure 3.26 Graphs of the exact and asymptotical expressions of the solution ne...
Figure 3.27 Solution
g
2
(
t
)
( 3.167 ) for a semi‐infinite contact region a = ∞.
Figure 3.28 Solutions for a finite (D, shaded lines) and semi‐infinite contact ...
Chapter 4
Figure 4.1 Elastic energy for uniaxial tension as a function of angle
Φ
.
Figure 4.2 Specific elastic energy for uniaxial tension as a function of angle
Figure 4.3 Elastic energy for pure shear as a function of angle
Φ
.
Figure 4.4 Specific elastic energy for pure shear as a function of angle
Φ
Figure 4.5 Direction‐dependent strength criterion
g
(Φ)
for a uniaxial load...
Figure 4.6 Specific, direction‐dependent strength criterion
g
(Φ)
for a uni...
Figure 4.7 Direction‐dependent strength criterion
g
(Φ)
for a pure shear lo...
Figure 4.8 Specific, direction‐dependent strength
g
(Φ)/
ρ
for a pure s...
Figure 4.9 Specific direction‐dependent ultimate stored energy for uniaxial ten...
Figure 4.10 Specific direction‐dependent ultimate stored energy for a pure shea...
Chapter 5
Figure 5.1 Driveshafts of a common passenger car.
Figure 5.2 Composite propshaft in a Renault Espace Quadra (Pollard, 1989 ).
Figure 5.3 Composite driveshaft (Keys et al., 2018 ).
Figure 5.4 Torsion of a composite driveshaft by the terminal torque M
T
.
Figure 5.5 Geometry of the cross‐section of the rod.
Figure 5.6 Types of fastening of the ends of the rod.
Figure 5.7 Driveshaft on the periodically spaced momentless supports.
Figure 5.8 Driveshaft on the periodically spaced rotation‐free supports.
Figure 5.9 Solid triangular and circular cross‐sections of the driveshaft of th...
Figure 5.10 Hollow triangular and circular cross‐sections of the driveshaft.
Figure 5.11 US3651661(A), 1972: “Composite shaft with integral end flange.”
Figure 5.12 US4171626(A): “Carbon fiber‐reinforced composite drive shaft.”
Figure 5.13 US4173128(A): Composite drive shaft.
Figure 5.14 US4551116(A): Drive shaft assembly.
Figure 5.15 US5725434(A): Shaft of fiber‐reinforced material.
Figure 5.16 US2017082149(A1): Composite driveshaft for a rotary system.
Chapter 6
Figure 6.1 Basic types of suspension.
Figure 6.2 Semi‐independent axles with Watt linkage wheel guide correction.
Figure 6.3 Semi‐independent axles.
Figure 6.4 Vehicle dynamics effects.
Figure 6.5 Roll center of semi‐independent axles.
Figure 6.6 Coordinate systems of vehicle (DIN ISO 8855).
Figure 6.7 Suspension geometry.
Figure 6.8Figure 6.8 Suspension geometry, projection on the
yz
‐plane.
Figure 6.9Figure 6.9 Suspension geometry, projection on the
xz
‐plane.
Figure 6.10 Suspension geometry, projection on the
xy
‐plane.
Figure 6.11 Bicycle model of the vehicle in an earth‐fixed coordinate system.
Figure 6.12 Side slip curve and lateral force properties.
Figure 6.13 Wheel slip angles in a single‐track model.
Figure 6.14 Slip angle and lateral force on the front wheel.
Figure 6.15 Slip angle and lateral force on the rear wheel.
Figure 6.16 Neutral steer in the bicycle model.
Figure 6.17Figure 6.17 Steer angle for low speed turning. “Ackermann” cornering...
Figure 6.18 Explanation of the understeer effect from the viewpoint of the bicy...
Figure 6.19 Explanation of the oversteer effect from the viewpoint of the bicyc...
Figure 6.20 US2002000703 (A1) Wheel suspension system with an integrated link, ...
Figure 6.21 EP2423012 (A2) Fiber composite anti‐roll bar, https://www.epo.org.
Chapter 7
Figure 7.1 Cornering of a car with stiff and with flexible rear axles.
Figure 7.2 Steering of vehicle with (a) absolutely rigid axle and (b) induced s...
Figure 7.3 Induced camber angle for a flexible rear axle (roll motion is not di...
Figure 7.4 Relationship between the rolling motion of the vehicle and twisting ...
Figure 7.5 Lateral shift of the wheel and additional steer angle due to centrif...
Figure 7.6 Relation between the torque M
TB
in the twist‐beam and the roll momen...
Figure 7.7 Suspension roll stiffness of a twist‐beam axle.
Figure 7.8 Lateral rigidity of a twist‐beam axle.
Figure 7.9 Camber stiffness of a twist‐beam axle.
Figure 7.10 Bending‐torsion and tensile‐torsion coupling for a composite fiber ...
Figure 7.11 Laminate structure in the cross‐beam for the countersteering compos...
Figure 7.12 H‐shaped and Π‐shaped cross‐sections.
Figure 7.13 Bucket design.
Figure 7.14 Representation of the cross‐beam in two views.
Figure 7.15 Display of the bucket design in two views.
Figure 7.16 Step‐by‐step assembly of the countersteering twist‐beam axle.
Figure 7.17 Finite‐element model of the countersteering twist‐beam axle.
Figure 7.18 All‐synthetic plastic concepts: twist‐beam rear suspension, Volkswa...
Figure 7.19 EP3174744B1, Motor vehicle suspension with glued composite torsion ...
Figure 7.20 DE202013004035U1 (2013): Assembly for a vehicle.
Figure 7.21 US6382649B1 (1999‐07‐16): Wheel suspension in a motor vehicle.
Figure 7.22 DE202016105937U1, “Chassis axle and vehicle.”
Chapter 8
Figure 8.1
Glass fiber reinforced plastic
(
GFRP
) springs: (a) fiberglass vol...
Figure 8.2 Helical composite spring, subjected to axial load and axial torque.
Figure 8.3 Helical spring loaded by torque and axial force.
Figure 8.4 Helical spring with variable wire diameter and non‐cylindrical form.
Figure 8.5 Middle surface
ϖ
of a free spring.
Figure 8.6 Middle surface
Ω
of a deformed spring.
Figure 8.7 Orientation of reinforcement fibers in the anisotropic conical sprin...
Figure 8.8 Orientation of two families of reinforcement fibers in the orthotrop...
Figure 8.9 Dependence effective circumferential modules
upon meridian angle
Φ
...
Figure 8.10 US20040256829A1 (2003) “Suspension system having a composite beam.”
Figure 8.11 EP0459220B1 (1993): “Ring‐shaped spring made out of fiber composite...
Figure 8.12 US4801019 (1989): “Shock Absorbing Unit.”
Figure 8.13 DE102009029300A1 (2009): “Plastic spring for a motor vehicle underc...
Figure 8.14 DE102012202625A1 (2013): “Plastic composite spring.”
Figure 8.15 US20030222385 (2003) “Composite wave ring spring.”
Chapter 9
Figure 9.1 Lateral surface and equivalent beam of the composite spring.
Figure 9.2 Composite spring (right) and its equivalent beam (left).
Figure 9.3 Contour plot of first fundamental frequency and critical loads as fu...
Figure 9.4 Critical loads as function of the degree of slenderness
ξ
durin...
Chapter 10
Figure 10.1 Leaf‐tension composite spring (a, c) and conventional leaf spring (...
Figure 10.2 Leaf‐tension composite spring.
Figure 10.3 ZF lightweight axle CLA. Source: Courtesy of ZF Friedrichshafen AG.
Figure 10.4 ZF CLA system (ZF Friedrichshafen AG, Press Information 2015).
Figure 10.5 Ratio of roll spring rate to vertical spring rate.
Figure 10.6 EP0660005A1 ( 1993 ) “Composite material leaf spring for motor veh...
Figure 10.7 DE102013003958A1 ( 2013 ) Storage arrangement of a transverse leaf...
Figure 10.8 DE102014215871 (2014) Vehicle axle with an axis extending in the in...
Figure 10.9 US2016/0347139A1 ( 2016 ) Transverse leaf spring for a motor vehic...
Chapter 11
Figure 11.1 Elements of a meander spring.
Figure 11.2 Different concepts of meander springs and a helical spring.
Figure 11.3 Anisotropic behavior of a meander compression spring: different sti...
Figure 11.4 Representation of the continuous meander spring and its replacement...
Figure 11.5 Directrix of a quarter of the neutral surface of a multiarc‐profile...
Figure 11.6 Moments and forces in the meander.
Figure 11.7 Mass ratio of an optimal spring to the mass of a spring with a cons...
Figure 11.8 Mass ratio of constant to optimal sinusoidal meander springs, see E...
Figure 11.9 WO1994018019A1 ( 1993 ‐02‐15) Suspension for the wheel of a vehicl...
Figure 11.10 WO8500207(A1) Springs for high specific energy storage.
Figure 11.11 WO8700252: Spring assemblies.
Figure 11.12 DE3641108C2: Spring element.
Figure 11.13 US4927124 Spring assemblies.
Figure 11.14 DE19962026A1 ( 2001 ): Spring/suspension device.
Figure 11.15 DE102012111252A1 (2012) Spring of suspension for a vehicle.
Figure 11.16 US2007267792A1 ( 2007 ) Sigma‐springs for suspension systems.
Figure 11.17 DE102008006411 ( 2009 ) Vehicle spring made from composite materi...
Figure 11.18 DE102008057463 ( 2008 ) Spring, particularly drawing and pressure...
Guide
Cover
Table of Contents
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Automotive Series
Advanced Battery Management Technologies for Electric Vehicles
Rui Xiong, Weixiang Shen
Noise and Vibration Control in Automotive Bodies
Jian Pang
Automotive Power Transmission Systems
Yi Zhang, Chris Mi
High Speed Off‐Road Vehicles: Suspensions, Tracks, Wheels and Dynamics
Bruce Maclaurin
Hybrid Electric Vehicles: Principles and Applications with Practical Perspectives, 2nd Edition
Chris Mi, M. Abul Masrur
Hybrid Electric Vehicle System Modeling and Control, 2nd Edition
Wei Liu
Thermal Management of Electric Vehicle Battery Systems
Ibrahim Dincer, Halil S. Hamut, Nader Javani
Automotive Aerodynamics
Joseph Katz
The Global Automotive Industry
Paul Nieuwenhuis, Peter Wells
Vehicle Dynamics
Martin Meywerk
Modelling, Simulation and Control of Two‐Wheeled Vehicles
Mara Tanelli, Matteo Corno, Sergio Saveresi
Vehicle Gearbox Noise and Vibration: Measurement, Signal Analysis, Signal Processing and Noise Reduction Measures
Jiri Tuma
Modeling and Control of Engines and Drivelines
Lars Eriksson, Lars Nielsen
Advanced Composite Materials for Automotive Applications: Structural Integrity and Crashworthiness
Ahmed Elmarakbi
Guide to Load Analysis for Durability in Vehicle Engineering
P. Johannesson, M. Speckert
Design and Analysis of Composite Structures for Automotive Applications
Chassis and Drivetrain
Vladimir Kobelev
Department of Natural Sciences, University of Siegen, Germany
Copyright
This edition first published 2019
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Library of Congress Cataloging‐in‐Publication Data
Names: Kobelev, Vladimir, 1959‐ author.
Title: Design and analysis of composite structures for automotive
applications : chassis and drivetrain / Vladimir Kobelev, Department of
Natural Sciences, University of Siegen, Germany.
Description: First edition. | Hoboken, NJ : Wiley, 2019. | Series: Automotive
series | Includes bibliographical references and index. |
Identifiers: LCCN 2019005286 (print) | LCCN 2019011866 (ebook) | ISBN
9781119513841 (Adobe PDF) | ISBN 9781119513865 (ePub) | ISBN 9781119513858
(hardback)
Subjects: LCSH: Automobiles–Chassis. | Automobiles–Power trains. |
Automobiles–Design and construction.
Classification: LCC TL255 (ebook) | LCC TL255 .K635 2019 (print) | DDC
629.2/4–dc23
LC record available at https://lccn.loc.gov/2019005286
Cover Design: Wiley
Cover Images: © Vladimir Kobelev, Background: © solarseven/ShuWerstock
Foreword
From a materials science point of view, composite materials of glass and carbon fibers have a specific potential and already some practical importance in several applications under high dynamic loads. Comparing the fibers, glass fibers are the better material for spring applications because their lower modulus of elasticity compared to carbon fibers. This is favorable in terms of high strokes and deformation requirements. Due to their high specific strength and the stiffness of composite materials, it is in principle possible to achieve weight savings of 30 – 70% of the weight of a steel spring depending on application. In addition to reduce the unsprung masses for suspension, it is also possible to improve driving dynamics as well as noise, vibration and hardness behavior (NVH), since the material properties are better in some significant areas. Furthermore, due to the high corrosion resistance and resistance against other environmental influences, surface protection is not necessary in most of the applications.
However, the usage of composite materials for springs have not reached high quantities due to some limitations. Load transmission requires special designs. Considering suspension coil springs, high loads transverse to the main load direction occur. Therefore, the load transmission does not follow ideally to the fiber direction and only medium loads can act on the matrix. In addition, in the case of large‐scale production and the available manufacturing processes, value adjustments must be made in comparison with units made of steel. These are currently the focus of research and development efforts throughout the world. Endless, unidirectional fiber materials, such as those used for structural elements in automotive engineering, exhibit strong anisotropic, i.e. direction‐dependent, properties. The fibers used are oriented with respect to the loads that occur. Therefore, the leaf spring, where loading results almost in tension stresses of the fibers is the perfect match with composite materials. Huge weight reduction up to 75% is possible to achieve by using the material properties and the design flexibility of glass fiber reinforced composite in the best way. A single composite tension leaf spring can substitute a steel multi‐leaf spring with a progressive spring load characteristic. The special design leads to a very homogenous, progressive spring characteristic and therefore, a better driving performance. Furthermore, we know already some designs for suspension steel coil springs substitution such as one‐by‐one substitution by composite coil spring and a meander spring design. In both case these springs do need special tools for the design and did not reach the market breakthrough due to huge different load‐rate requirements within the platforms.
There are some processes existing for the production of glass fiber composite springs. Nevertheless, the prepreg process (pre‐impregnated fibers) has proven itself as the best due to the realizable good properties under dynamic loads. Prepreg processes result in an optimal adhesive strength due to low porosity and allows flexibility in design, such as geometry, width and height of the spring. It is also possible to produce the elements of chassis in general and suspension particular using the resin injection process. For this resin injection process, a fiber structure is first produced from the dry reinforcement fibers, which follows the desired component geometry. If required, structural cohesion can be achieved using textile methods, such as sewing or bonding, which bond the fibers together. Such fiber structures are called preforms. The injection of the resin influences the orientation of the fibers and therefore, those springs do not reach the performance of prepreg composites due to potential ondulation.
Automotive manufacturers' requirements for carbon dioxide reduction, lower vehicle weight, the reduction of unsprung masses and the robustness of the springs, especially in the event of corrosion, will further increase in the future. The optimal application of the materials used plays a decisive role, supported by material properties, best technology and processes as well as an efficient design. Therefore, alternative materials, such as composites, may become higher importance for dynamic loaded suspension applications.
Prof. Dr. Vladimir Kobelev was born in Rostow‐na Donu, Russian Federation. He studied Physical Engineering at the Moscow Institute of Physics and Technology. After his PhD at the Department of Aerophysics and Space Research (FAKI), he habilitated at the University of Siegen, Scientific‐Technical Faculty. Today, Prof. Kobelev is lecturer and APL professor at the University of Siegen in the subject area of Mechanical Engineering.
In his industrial career, Prof. Kobelev is an employee at Mubea, a successful automotive supplier located near Cologne/Germany. In the Corporate Engineering Department, Prof. Kobelev is responsible for the development of calculation methods and physical modeling of Mubea components.
Joerg Neubrand
CTO, Managing Director and
Member of the Executice Board of the Mubea Group
Series Preface
Fuel efficiency continues to “drive” significant research and development in the automotive sector. In many instances, this is propelled by regulations that target reduced emissions as well as reduced fuel consumption. Even with more efficient vehicles and electric hybrid or purely electric driven systems, the need for reduced energy consumption is demanded by the market. This is due to the fact that the customer base is demanding increased efficiency as this brings better performance, lower costs and extended range of the vehicle. One clear means by which fuel efficiency can be enhanced is by reducing the weight of the vehicle. Lightweighting can be accomplished by a number of means, one of which is lighter weight material substitution. That is to say, one may substitute a lighter material for a heavier one on a vehicle component. Composites have been used to replace metal components in efforts to lightweight aircraft for decades. More recently, advances in materials, manufacture, and design have made composites cost effective and viable in the automotive sector. Two major stumbling blocks that have hindered composite use in the automotive sector are the cost of the composite components, and the ability to rapidly and economically produce such components in quantities that are needed by the automotive sector. Recently, these stumbling blocks have been overcome. However, for most commercial automotive applications, composites remain relegated to less critical elements of the vehicle system such as body panels. The use of composite for more critical vehicle applications such as suspension and drive train elements have been left to extremely demanding automotive scenarios such as Formula One. However, this scenario is about to change.
Design and Analysis of Composite Structures for Automotive Applications, provides an in‐depth technical analysis of critical suspension and drive train elements with a focus on composite materials. This includes basic principles for the design and optimization of critical vehicle elements using composite materials, as well as classical concepts related to mass reduction in automotive systems. The author, Professor Kobelev, skillfully integrates concepts related to vehicle parameters such as stiffness into overall vehicle dynamics using closed form solutions that are described in exquisite detail. The discussions focus on key elements of the vehicle including suspension and powertrain. These discussions are both comprehensive as well as the first of their kind in a text book, making this text an important reference for any automotive engineer on the leading edge.
Design and Analysis of Composite Structures for Automotive Applications is part of the Automotive Series that addresses new and emerging technologies in automotive engineering, supporting the development of next generation vehicles using next generation technologies, as well as new design and manufacturing methodologies. The series provides technical insight into a wide range of topics that is of interest and benefit to people working in the advanced automotive engineering sector. Design and Analysis of Composite Structures for Automotive Applications is a welcome addition to the Automotive Series as it primary objective is to supply pragmatic and thematic reference and educational materials for researchers and practitioners in industry, and postgraduate/advanced undergraduates in automotive engineering. The text is a state‐of‐the art book written by a leading world expert in composites and its application to suspensions and is a welcome addition to the Automotive Series.
Thomas Kurfess
March 2019
List of Symbols and Abbreviations
E
L
Longitudinal modulus of elasticity of composite parallel to fiber direction
E
T
Transverse modulus of elasticity of composite perpendicular to the fiber direction
G
TL
Transverse‐longitudinal shear modulus of composite
G
TT
Transverse shear modulus of composite
r
f
Radius of the fiber
External radii of hypothetical matrix cylinders
V
f
Fiber volume content
V
m
Matrix volume content,
V
m
= 1 −
V
f
ν
TL
Transverse‐longitudinal Poisson ratio of a composite
ν
TT
Transverse Poisson's ratio of a composite
E
f
Longitudinal modulus of elasticity of fibers
E
f
.
T
Transverse modulus of elasticity of fibers
E
m
Modulus of elasticity of matrix (resin)
ν
m
Poisson's ratio of matrix (resin)
G
m
Shear modulus of matrix (resin)
G
f
.
TL
Transverse‐longitudinal shear modulus of fibers
ν
f
.
TL
Transverse‐longitudinal Poisson's ratio of fibers
ν
f
.
TT
Transverse Poisson's ratio of fibers
S
= [
S
ijpq
]
Compliance tensor of rank four,
i
,
j
,
p
,
q
= 1, 2, 3
C
= [
C
ijpq
]
Elasticity tensor of rank four
C
(0)
= [
c
ijpq
]
Elasticity tensor of rank four, in the layer coordinate system
S
(0)
= [
s
ijpq
]
Compliance tensor of rank four, in the layer coordinate system
I
= [
I
ijpq
]
Fourth rank identity tensor
σ
Voigt's stress vector
ɛ
Voigt's strain vector
C
Voigt's elasticity matrix
Kelvin's stress vector
Kelvin's strain vector
Kelvin's elasticity tensor
S
(0)
Compliance matrix in Voigt's notation in intrinsic coordinates
Compliance matrix in Kelvin's notation in intrinsic coordinates
t
= [
t
lk
]
Transformation (rotation) square 3×3 or 2×2 matrix
T
σ
σ‐transformation (rotation) square 6×6 matrix, in Voigt's notation
T
ε
ε‐transformation (rotation) square 6×6 matrix, in Voigt's notation
Transformation (rotation) square 6×6 matrix, in Kelvin's notation
A
Plane modulus quadrant, square 3×3 matrix (entries for the membrane elasticity tensor) in Voigt's notation
B
Coupling quadrant, square 3×3 matrix (entries for the coupling elasticity tensor) in Voigt's notation
D
Plate quadrant, square 3×3 matrix (entries for the bending elasticity tensor) in Voigt's notation
ɛ
T
= [
ε
11
,
ε
22
,
γ
12
= 2
ε
12
]
Strain vector in Voigt's notation
κ
T
= [
κ
11
,
κ
22
, 2
κ
12
]
Curvature vector in Voigt's notation
N
T
= [
N
11
,
N
22
,
N
12
]
In‐plane forces vector in Voigt's notation
M
T
= [
M
11
,
M
22
,
M
12
]
Bending moments vector in Voigt's notation
Q
Reduced stiffness matrix in Voigt's notation
σ‐transformation (rotation), square 3×3 matrix in Voigt's notation
ε‐Transformation (rotation) square 3×3 matrix in Voigt's notation
Plane modulus quadrant, square 3×3 matrix (entries for the membrane elasticity tensor) in Kelvin's notation
Coupling quadrant, square 3×3 matrix (entries for the coupling elasticity tensor) in Kelvin's notation
Plate quadrant, square 3×3 matrix (entries for the bending elasticity tensor in Kelvin's notation
Strain vector in Kelvin's notation
Curvature vector in Kelvin's notation
In‐plane reaction forces, vector in Kelvin's notation
Bending moments, vector in Kelvin's notation
Reduced stiffness matrix in Kelvin's notation
Transformation matrix for rotation (3×3) in Kelvin's notation
X
t
,
X
c
Tensile or compressive strengths in the fiber direction
Y
t
,
Y
c
Tensile or compressive strengths in the transverse direction
Matrix of the Mises–Hill criterion, Voigt's notation in intrinsic coordinates
F
,
G
,
H
,
L
,
M
,
N
Characteristic values of the Mises–Hill criterion
Λ
i
Eigenvalues of the Mises–Hill criterion,
i
= 1..6
Ultimate normal stresses in the Mises–Hill criterion
Ultimate shear stresses in the Mises–Hill criterion
Matrix of the Mises–Hill criterion, Kelvin's notation in intrinsic coordinates
Φ
Rotation angle of fibers in the plane “1–2”
Matrix of the Mises–Hill criterion in the rotated axes, Kelvin's notation
Matrix of the pressure‐sensitive Mises–Hill criterion, Voigt's notation in intrinsic coordinates
Matrix of the pressure‐sensitive Mises–Hill criterion, Kelvin's notation in intrinsic coordinates
F
(2)
,
F
(4)
,
F
(6)
Tensors of the 2nd, 4th and 6th ranks of the Goldenblat–Kopnov tensor fracture criterion
σ
f
Axial stresses in cylindrical fibers
σ
m
Axial stresses in hollow matrix cylinders
τ
Shear stress at the fiber surface
τ
p
Yield point of the matrix
p(
z
), q(
z
)
Auxiliary functions, p =
u
m
−
u
f
, q =
u
m
+
u
f
.
u
m
,
u
f
Axial displacements of matrix and fiber cylinders
λ
,
μ
,
Parameters of the length dimension
Parameters of the inverse length dimension
l
p
Length of the plastic zone
R
f
,
R
f
Crack extension resistance of fibers and matrix
Auxiliary modules
K
f
,
K
m
Fracture toughness of fibers and matrix
d
U
e
/
da
Energy release rate per thickness unit
d
U
f
/
da
Crack extension resistance per thickness unit
ϕ
i
(
ρ
,
η
)
Potential functions,
i
= 1, 2
a
=
l
c
/2
r
f
Dimensionless length of adhesive or debonding region
K
max
,
K
max
Maximum and minimum stress intensity factor
Y
(
a
)
Dimensionless parameter that reflects the geometry
c
f
=
c
f
(
R
σ
)
Material constant of matrix or resin for a given stress ratio
R
σ
R
σ
=
K
min
/
K
max
Stress ratio of cyclic load
p
c
(
K
) =
K
−
p
Paris–Erdogan crack propagation function
C
T
Torsional rigidity of bar (driveshaft)
I
b
1
,
I
b
2
Moment of inertia of cross section with respect to both bending axes
Critical torque in Greenhill's problem
W
e
(Φ)
Density of elastic energy
W
e
*
(Φ)
Elastic energy per mass unit (specific elastic energy)
Ultimate elastic energy per mass unit (specific ultimate elastic energy)
Ultimate elastic energy
X
E
,
Y
E
,
Z
E
Axes of the earth‐fixed coordinate system
X
V
,
Y
V
,
Y
V
Axes of the vehicle‐fixed coordinate system
X
,
Y
,
Z
Axes of the horizontal coordinate system
X
W
,
Y
W
,
Z
W
Axes of the wheel coordinate system
ϕ
Roll angle
θ
Pitch angle
ψ
Yaw angle
β
Sideslip angle of a vehicle
ς
=
ψ
−
β
Course angle
S
X
;
V
Circumferential slip
ω
Rotational speed of a wheel
ω
0
The rotational speed of a straight and freely rolling wheel
α
Sideslip angle of a wheel
μ
X
,
W
Coefficients of circumferential force
μ
Y
,
W
Coefficients of lateral force
C
α
Cornering stiffness
C
αf
,
C
αr
Cornering stiffness of front and rear tire
I
z
Mass moment of inertia of the vehicle around the vertical axis
m
Mass of a vehicle
L
f
Horizontal distance from front axle to center of mass
L
r
Horizontal distance from rear axle to center of mass
L
w
=
L
f
+
L
r
Wheel base
δ
Steer angle at the wheel (part of steer angle due to steer)
Steer angle gradient
δ
a
Steer angle according to Ackermann
Δ
V
External excitation in the course of steering
ω
V
Yaw circular frequency of a vehicle
D
V
Damping factor of a vehicle's yaw oscillation
L
0
Free length of a helical spring
L
rel
Released length of a helical spring
L
comp
Compressed length of a helical spring
L
c
Close up length of a compressed spring
s
=
L
rel
−
L
comp
Spring travel
c
Axial compression or extension spring constant
c
θF
Compression‐twist spring rate
c
θ
Twist spring rate
U
e
Elastic energy
U
f
Work of applied forces
F
Axial force on a helical spring
M
θ
Axial torque on a helical spring
c
*
Design value for a spring constant
τ
w
Ideal stress at solid height
d
opt
Optimal diameter of a wire
m
opt
Lower boundary for spring mass
ϖ
Middle surface of an undeformed conical spring
Ω
Middle surface of a deformed conical spring
t
c
Thickness of an anisotropic conical spring
r
a
,
r
b
Inner and outer radius of the middle surface of a free conical spring
R
a
,
R
b
Outer radius of the middle surface of a deformed conical spring
Δ =
r
b
/
r
a
Ratio of the outer radius to inner radius of a conical spring
Inversion point of a conical spring
z
a
,
z
b
Heights of the inner and outer edges of a free spring
Z
a
,
Z
b
Heights of the inner and outer edges of a deformed spring
ε
1
Circumferential mid‐surface strain of a conical spring
κ
1
Circumferential curvature changes of a conical spring
Effective elastic modulus
Effective orthotropic elastic modulus
s
Q
=
s
b
+
s
s
Total transversal displacement of a helical spring
Q
Shear force of equivalent column for a helical spring
M
B
Bending moment of a helical spring
m
B
External torque per unit length of a helical spring
f
Q
External load in the transverse direction of a helical spring
C
44
I
T
Twist stiffness of a wire with respect to its axis
C
33
I
b
Stiffness of a spring wire in the case of bending in a binormal direction
C
33
I
n
Stiffness of a spring wire in the case of bending in a normal direction
s
o
(
z
)
Initial transverse deflection of a helical spring
v
o
(
z
)
Initial transverse velocity of a helical spring
ω
k
Circular natural frequency in the order of
k
of a helical spring
ξ
=
L
0
/
D
Slenderness ratio of a helical spring
μ
=
L
/
L
0
Dimensionless length of a helical spring
Ω
k
Dimensionless frequency of transverse oscillations in the order of
k
of a helical spring
Critical deflection during compression from the free length of a helical spring
Critical deflection during expansion from the flattened state of a helical spring
f
(
σ
eff
,
t
)
Anisotropic stress function for creep
t
Time for creep
Deviatoric component of creep strain
s
ij
Deviatoric component for creep stress
σ
eq
Mises equivalent stress
c
τ
Creep constant for shear strain
c
σ
Creep constant for uniaxial strain
γ
e
Elastic component of shear strain
γ
c
Creep component of shear strain
Torque at the moment
t
= 0
M
T
(
t
)
Torque as a function of time
Spring force at the moment
t
= 0
F
z
(
t
)
Spring force as a function of time
Bending moment at the moment
t
= 0
M
B
(
t
)
Bending moment as a function of time
Φ
T
(
t
),Φ
B
(
t
),Φ
H
(
t
)
Relaxation functions for twisting, bending and helical spring
f
′
=
∂f
/
∂z
, or
∂f
/
∂x
1
, or
∂f
/
∂ξ
1
“Prime” denotes a derivative with respect to a coordinate:
z
, or
x
1
, or
ξ
1
“Dot” denotes a time derivative
Abbreviations
AF
Aramid fiber
AFRP
Aramid fiber reinforced plastic
Autoclave
Heated pressure tank
CE
Cyanate ester resin
CF
Carbon fiber
CFRP
Carbon fiber reinforced plastic
DSA
Driveshaft axis
EP
Epoxy resin
Fabric
Biaxially woven textile
FRP
Fiber reinforced plastic
GF
Glass fiber
GFRP
Glass fiber reinforced plastic
HM
High modulus
HT
High tensile strength
Laminate
Layer construction of cured, individual plies
Matrix
Resin in which the fibers are embedded
NVH
Noise, vibration and hardness
PA
Polyamide
PEEK
Polyetheretherketone
PF
Phenolic resin
PMMA
Polymethyl‐methylacrylate
PPS
Polyphenyl sulfide
Prepreg
Preimpregnated fibres – fibers or textiles pre‐saturated with resin
PU
Polyurethane resin
Roving
Soft strand of twisted, attenuated, freed of external matter fiber ready to conversion into yarn
RTM
Resin transfer molding – resin is injected into an enclosed mold in which fibers have been placed
Tg
Glass transition temperature
UD
Unidirectional fibers are oriented in only one direction
UP
Unsaturated polyester
VE
Vinyl ester resin
Introduction
Composites in Automotive Chassis and Drivetrain
In times of climate change and rising emissions in the environment, lightweight construction has found its way into almost all industries. The authorities, particularly in the automotive industry, formulate endlessly decreasing targets in emission reduction. Because increasingly stringent emissions can be minimized through weight reduction, an optimal structural design made with lightweight materials is one of the principal tendencies in contemporary development of passenger cars. Some of the most attractive improvements have been seen in the use of composites to replace parts and components traditionally manufactured from steel (Miravete 1996; Tucker and Lindsey 2002). In particular, carbon‐fiber‐reinforced plastics and glass reinforced plastics have great potential to reduce the weight of passenger cars. Cost of a product remains a key issue. As with any lightweight material, all further expenses, which are incurred in addition to the cost of the base material, must be accounted for. The major task to make the product attractive to customers and the market is to reduce lightweight construction and production costs as much as possible along with significant weight reduction and other extra benefits. Despite manufacturing processes being continuously improved, there is still substantial progress to be made for cost‐effective mass production. Safety is another dominant criterion for passenger cars. Hence, new designs must be structurally robust enough to adhere to current and future crash safety targets.
Over recent years, car body and drivetrain have come under deep examination in the attempt to reduce mass of structure and a range of innovative concepts have been developed (Kedward 2000; Brooks 2000; O'Rourke 2000). Lightweight construction has become an optimization goal that is valid for several components of automobiles (Lu and Pilla 2014a, 2014b, 2014c; Elmarakbi and Azoti 2015; Njuguna 2016; Ishikawa et al. 2018; Hayashi 2000; Nomura 2000).
Weight reduction of the chassis has gained in importance as well. The chassis has a substantial potential of weight reduction (Neubrand 2014). Among other lightweight materials for chassis design, glass‐fiber‐reinforced plastic provides a good alternative to steel. Moreover, the unsprung mass can be lessened. This factor brings distinct advantages for the driving dynamics and comfort.
As previously mentioned, reducing weight of vehicles is an indispensable requirement in the automotive manufacturing sector. There are several “material factors” that are used for characterization of weight reduction (Ashby 2010). Apparently, the material density is the most trivial material factor in determining the best suited material for a certain application. The density determines the relative weights of structures, but provides no information about their strength and flexibility. Another, also simple factor is the material price of the mass unit. The specific price factor determines the material that is best suited for a price‐critical application. The price factor, as a sum of raw material price and manufacturing expenses, is commercially important in material evaluation.
Another factor is the specific strength, or the strength‐to‐weight ratio of the material. The specific strength of an isotropic material is obviously given by the tensile or yield strength divided by the density of the material. A material with a high specific strength will be suitable for load‐carrying elements. There are several secondary criteria of this kind, which depend upon the art of dominant load: uniaxial stress or bending stress. The specific strength factors distinguish whether axial stress or stress due to bending dominates. In the first case, stress is constant over the cross‐section of the part. Specific strength is equal to tension load divided by the cross‐sectional area and density of the material. In the second case, stress is a linear function of the thickness coordinate. The specific strength is equal to the bending moment is divided by the resistance moment and density of the material. For the fixed weight of material, the thickness of the material with a lower density is greater. The resistance moment for the material with the lower density is greater as well. Accordingly, the material with lower density possesses higher specific strength for bending even for the equal ultimate strength of both materials. This remark makes the application of lighter materials attractive for bending‐dominated applications. Similar speculations are applicable for a shaft loaded by the given torque. In this load case, the shear stress depends linearly on the radius, and a material with lower density leads to lower stress on the surface if the torque and mass of the shaft are prescribed.
The specific stiffness is basically the elastic module‐to‐density ratio of the material (Ashby 2010). The specific strength of an isotropic material is given either by the Young's modulus divided by the density of the material for the elements predominantly in a uniaxial tension or compression state or by the shear modulus divided by the density of the material for the elements mainly in a state of shear. A material with a high specific stiffness will be suitable for elements that guarantee maximal stiffness. For example, the specific stiffness characterizes the performance of materials for structural elements that are responsible for buckling performance, dynamic and static stiffness, and for aeroelastic critical applications. Analogous to the specific strength, the specific stiffness distinguishes whether the uniaxial stress or stress due to bending dominates. For example, compare two materials in a state of bending or torsion with equal elasticity modules, but different densities. If we assume that both elements have equal mass, the specific stiffness of the lighter material is higher than the stiffness of heavier material. This occurs because the plate thickness or shaft diameter made of a material with the lower density is higher. Accordingly, the corresponding bending or torsional stiffness will be higher. These conjectures make the application of composites preferable for structural elements in bending or torsion stress states.
The elements that provide energy storage must be characterized by specific energy density. The ratio of specific energy density to mass density of a material characterizes the material for energy harvesters, different springs and flexible structural elements of an automotive chassis. These conjectures about the preferably light material in the states of torsion or bending are generally not valid for specific energy density. The argument is as follows. Consider, for example, two shafts (torsion springs) with the equal mass, equal shear modulus, equal applied torque, but two different densities. The shaft made of the lighter material possesses the higher diameter and also has the greater torsion stiffness. The twist for the given torque will be lower. Consequently, the stored energy of the lighter shaft is lower if the torque is given. But simultaneously the maximal stress will be lower, because the resistance moment of the shaft with the higher diameter is higher. The specific energy density in the case of torsion is roughly the ratio of the squared ultimate stress in the material divided by the density and elasticity modulus. The most favorable application of one or other material also depends on the load character. If the material is anisotropic, the formulas for calculation of specific factors will be somewhat complicated. These thoughts will be explained in detail later in the book.
There are other specific material parameters in the automotive praxis. Among others, the specific plastic energy release rate. This material parameter is applied for car body design. Specific plastic energy release rate indicates the suitability of the material for applications in the zones of energy adsorption. The materials with the higher specific plastic energy release rate behave preferably in the event of an accident.
Therefore, the advanced specific “performance‐to‐density” ratios are essential for comparison of engineering materials in engineering design. These factors include Young's modulus to density, Young's modulus to specific price, strength to density, strength to toughness, strength to elongation, strength to cost, strength to maximal service temperature, specific stiffness to specific strength, electrical resistivity to cost, recycle fraction to cost and energy content to cost (Ashby 2010). The specific factors deal commonly with the uniaxial tensile load and therefore are scalars. If the stresses are multi‐axial and alternating, the scalar performance‐to‐density factors provide only rough estimations of design efficiency.
Moreover, the majority of “material factors” was developed for isotropic materials and takes no notice of the anisotropy of composite materials. Anisotropy is characterized by the fact that there is a shear‐stretch coupling. This means that a normal stress in the longitudinal direction additionally causes a displacement. Similarly, a shear stress additionally causes an elongation. In other words, the fiber‐reinforced composite materials have habitually different stiffnesses in diverse load directions. The use of scalar factors for materials with strong anisotropy and variable stress fields delivers, as a rule, an unreliable estimation of design features. The reliable optimal design of a composite material must be based on a deep structural analysis and comprehensive exertion of the specific advantages of composite materials.
Physical Properties of Composite Materials
A material is referred to as a composite if at least two diverse components are combined on the microscopic level to a new concrete mixture. The separate substances, based on their various properties, accomplish different tasks. By their nature, dissimilar materials are also frequently joined so the combination gains remarkable properties that both components cannot achieve separately. Comprehensive surveys of the physical properties and manufacturing of composites have been given (Peters 1998; Kelly and Zweben 2000; Kleinholz et al. 2010; Neitzel et al. 2014; ECSS‐E‐HB‐32‐20 2011).
Specifically, “composite” generally refers to solid combinations of high‐strength, but brittle reinforcement fibers embedded in a weak, but ductile matrix (Figure 1). The synergy effect is that the properly synthesized composite inherits the high stiffness and load capacity from fibers and high ductility from the matrix.
Figure 1 Types of composite material: (a) reinforcement by short fibers or whiskers; (b) unidirectional composite, reinforced by continuous fibers and (c) multilayered, laminated composite made of multiple layers.
Chemical industry produces artificial fibers, for example, carbon, glass or aramid fibers. These fibers possess outstanding mechanical and chemical properties. Matrix materials are being steadily developed as well. The raw materials for fibers are usually very brittle and possess only a restricted strength. However, as the fiber diameter decreases, the strength increases tremendously. The explanation of the increase in strength is comprehended in the size effect. The size effect unfolds within the remarkable features. On the one hand, the size of the flaw is limited in a thin fiber. The flaw must be many times smaller to generate an endless fiber. According to statistical considerations, the length of a flawless fiber section continues to grow for thin fibers. In other words, the thinner the fiber, the longer the flawless area (Argon 1974).
Consider a large, bulk body; for example, a glass pane. The number and size of individual defects increase with the size of the component. There are numerous dilute defects in the large volumes of the homogenous material. These initially existing defects make the homogenous material brittle. The material fails to arrest the small initial cracks. The crack grows unrestricted through the volume and finally provokes instant fracture. For the destruction of a bulk homogenous part, the principle of the weakest link is applicable. Namely, the principle of the weakest link is based on the size effect. The weakest link principle declares that a chain is only as strong as its weakest link. This means that if a part contains a defect it breaks. In application to fibers of composite materials, if a fiber contains a defect it breaks.
The picture of fracture of a heterogeneous composite material is different. Several hundred thousand fibers are present in parallel in one bundle and if one fiber breaks, the other remains intact and continues to carry the full load. Thus, the load from the failed fiber redistributes to the many fibers without failure of the bundle. The stiffness of material alters with size as well. Accordingly, a material in fiber form has significantly higher rigidity and strength than a raw material. The smaller the fiber cross‐section, the higher its strength.
In fiber‐reinforced plastics, the mechanical properties, such as stiffness and strength, are determined primarily by reinforcement fibers. The fibers are made of a variety of materials, and processed to form diverse semi‐finished products.
For the production of fiber‐reinforced plastics, mostly inorganic fibers, such as glass fibers as well as carbon fibers or aramid fibers, are used. The carbon‐fiber‐reinforced polymer is an evolving construction material that exhibits exceptional mechanical properties, such as strength and rigidity, with light material density at the same time. The commercial production of carbon fibers started in the 1970s. Application was primarily in the aviation and aerospace industry. The carbon fibers invaded motorsport at the beginning of the 1980s (O'Rourke 2000
