Composite Structures: Zhao Liu, Jiahai Lu, Ping Zhu
Composite Structures: Zhao Liu, Jiahai Lu, Ping Zhu
Composite Structures: Zhao Liu, Jiahai Lu, Ping Zhu
Composite Structures
journal homepage: www.elsevier.com/locate/compstruct
a r t i c l e i n f o a b s t r a c t
Article history: Considering the crashworthiness and lightweight requirements in automotive industry, composite mate-
Available online 4 January 2016 rials have been gaining increasingly more attention for their high specific strength, high specific stiffness
and high energy absorption capability. Bumper system is one of the main structures which protect cars
Keywords: from the front and rear collisions. It is an effective way to develop the bumper system using composite
Composite bumper beam materials to meet the crash safety and lightweight demands simultaneously. However, the application of
Particle swarm optimization composite material also introduces great challenges into the optimization design process, such as com-
Kriging
plex non-linear material behavior, multi-working conditions and large amount of design variables. In this
Structure optimization
Finite element simulation
paper, a structure design and optimization method is proposed for a commercial front bumper system
made by carbon fiber woven composite. An integrated bumper system structure is presented considering
the manufacturing process of composite material. Then, an optimization procedure incorporating the
Kriging modeling technique and a modified PSO algorithm is proposed to find the optimal combination
of design variables. The real vehicle experiment proves that the optimized bumper system meets all the
requirements on strength and crashworthiness while with 31.5% weight reduction. The results reveal that
the proposed design method is an efficient and effective way for composite structure design.
Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction gaining increasingly more attention for their high specific strength,
high specific stiffness and high energy absorption capability. As a
Automotive crashworthiness is regarded as one of the most class of typical composites, fiber reinforced plastic (FRP) has been
important design considerations [1–4]. In most of the collision widely adopted to reduce the weight of the vehicle structure [7].
accidents, bumper system is the first vehicle component involved However, the application of composite materials also intro-
in the impact and protects the car body and passengers to a certain duces a great challenge into the optimization design process, such
extent. It is expected to be deformable enough to absorb the as complex non-linear material behavior, multi-working condi-
impact energy while possessing sufficient strength and stiffness tions and large amount of design variables. Hosseinzadeh et al.
to protect its nearby components [5]. Furthermore, with increasing [8] investigated a bumper beam system made of glass mat thermo-
need for energy conservation and environmental protection, light- plastic. The structure of the bumper beam was designed and veri-
weight design of vehicle structure has gained more and more fied based on the finite element analysis method considering the
attention in automotive industry [6]. Generally, material replace- low-velocity impact performance. Davoodi et al. [9] focused their
ment, structural optimization method and advanced manufactur- attention on improving the performance of a car bumper system
ing technology can be employed during the lightweight design using a hybrid kenaf/glass fiber composite. The results showed
process, in which material replacement is regarded as the most the benefits of using hybrid natural fiber in structural components
effective approach. When incorporating weight saving and crash- of a car. Davoodi et al. [10] and Belingardi et al. [11] paid their
worthiness requirements for developing automotive safety compo- attentions on selecting the best geometrical parameters of bumper
nents, such as the bumper system, composite materials have been structure to fulfill design requirements. Belingardi et al. [5] devel-
oped an integrated crash box and bumper beam system which had
⇑ Corresponding author at: State Key Laboratory of Mechanical System and better crashworthiness. Major parameters, such as impact energy,
Vibration, Shanghai Jiao Tong University, Shanghai 200240, PR China. Tel./fax: +86 peak load, energy absorption and so on were employed as
21 34206787. evaluation criteria. The effectiveness of the proposed structure
E-mail address: pzhu@sjtu.edu.cn (P. Zhu).
http://dx.doi.org/10.1016/j.compstruct.2015.12.031
0263-8223/Ó 2016 Elsevier Ltd. All rights reserved.
Z. Liu et al. / Composite Structures 140 (2016) 630–643 631
was interpreted by finite element simulations. Although previous D3410 for quasi-static test, cubic specimen was most frequently
researchers have put forward some effective composite bumper applied for both quasi-static and dynamic tests [15,16]. In the pre-
versions, the optimization concept has not been incorporated into sent study, the cubic specimen was designed according to the
the design process because of large amount of design variables, requirement of test equipment. Configurations of specimens were
multi-working conditions and high computational cost. shown in Fig. 1. Due to the reinforcement type, the transverse
For a composite bumper system, both geometrical parameters direction properties are considered to be identical to the longitudi-
and material parameters can be included as design variables. The nal ones. Thus, experiments were only conducted at 0° direction.
geometry parameters can be decomposed into shape variables, From the results, it can be seen that the in-plane mechanical
for instance the size of the cross-section, and thickness variables. properties of the studied carbon fiber woven composite show
The material parameters consist of laminate stacking sequence, apparent tension/compression asymmetry and anisotropic charac-
types of the fiber, reinforcement percentage, and so on. It is too teristics. The strain rate also has an effect on the in-plane mechan-
complicated and difficult to consider all the parameters concur- ical properties of the composite. The large difference of mechanical
rently in the optimization procedure. Multi-load cases and associ- properties between tension and compression may be caused by
ated high computational cost also restrain the proceeding of the tension/compression asymmetry characteristics of the carbon fiber
structural optimization design, especially for crash conditions with and different failure patterns under the tensile and compressive
high-nonlinearity performance and fragmentation absorption loading conditions [15,17].
mechanism. In contrast to metallic materials, laminated compos- In order to predict the material strength under different strain
ites possess more distinctive failure modes than metals [12–14], rates, the following two phenomenological models are applied to
which result in high complexity of structural optimization design quantify the strength property within the considered strain rate
of CFRP components. range:
In this paper, experimental work is firstly conducted to obtain
the mechanical properties of the studied carbon fiber plain weave rd ¼ rs ð1 þ C 1 expðlog10 ðe_ ÞÞ þ C 2 ðexpðlog10 ðe_ ÞÞÞ2
þ C 3 ðexpðlog10 ðe_ ÞÞÞ Þ
3
composite. Based on the tested results, constitutive model consid- ð1Þ
ering tension/compression asymmetry and anisotropy is proposed
with experimental verification. Then, considering the characteristic 2 3 !
e_ e_ e_
of the studied composite material and manufacturing process, an rd ¼ rs 1 þ C 1 ln _ þ C 2 ln _ þ C 3 ln ð2Þ
integrated bumper system structure is presented. After that, an
e0 e0 e_ 0
optimization procedure incorporating the Kriging modeling tech- in which e_ is the corresponding strain rate, and e_ 0 is the referential
nique and a modified PSO algorithm is proposed to find the optimal strain rate, which is defined as 0.001 s1 here. Eq. (1) is used to fit
combination of both the shape and thickness variables. Real vehi- the strength property of tension in the axial direction, while
cle experiments are conducted to verify the optimal design of the Eq. (2) is applied to the other two cases. Table 3 gives the fitted
bumper system. parameters. The precision of the fitted results is validated by the
determination coefficient, R2 . Remarkable consistency can be
2. Material characterization tests observed between the fitted and experimental results.
The material used in the present study is carbon fiber plain In order to consider the effect of strain rate, tension/compres-
weave composite. Its fiber is TC33 carbon fiber made by Tairyfil sion asymmetry and anisotropic characteristics, a user defined
Corporation. The matrix material is LY1564 SP/Aradur3486 from material model was established in this study.
Huntsman, in which LY1564 SP is implemented as the resin and For elastic condition, the stress–strain relationship is expressed
Aradur3486 as the hardener. The fabric is prepared as plain weave in the anisotropic form as,
pattern with 3 k fibers in a tow. The basic properties of the carbon 8 98 9
8 9
> 1
mE21 >> r1 >
< e1 >
fiber and the matrix are presented in Table 1. > > 0 >
= < E11 22 =< =
Composite sheets are manufactured by vacuum infusion pro- e2 ¼ mE1211 1
0 r2 ð3Þ
>
: > > E22
>>
>: >
cess with a curing time of 5 h at 80 °C. The weight fraction of car-
e4 ; >
: 0 0 1 ; r4 ;
bon fiber is 55%. The mechanical properties of the composite G12
material under both quasi-static and high strain rate are given in
in which E1 ¼ Eþ
when direction 1 is under tension, and E1 ¼ E
1 1
Table 2. Quasi-static tensile test at the axial direction was con-
when under compression; E2 ¼ Eþ 2 when direction 2 is under ten-
ducted according to ASTM D638, and shear test according to ASTM
sion, and E2 ¼ E 2 when under compression.
D3518. For there are no consistent standards on dynamic tensile
In order to predict the loading capacity of composite structure, a
and shear tests, specimens for dynamic tensile and shear tests
strength criterion should be implemented to describe the failure of
were conducted according to the requirement of testing equip-
composite material. The World-Wide Failure Exercise [18] has
ments and recommendations of literatures [15]. For compression
tested the predictability of the most commonly used failure criteria
tests, even though standard specimen was recommended in ASTM
based on identical experimental data and shown that all the tested
failure criteria illustrated limited predictive accuracy for all the
experimental results. Moreover, the experimental results are basi-
Table 1
Basic properties of the carbon fiber and the matrix. cally from unidirectional composite materials, which demonstrate
much different mechanical performance from woven composites.
Constituent Type Tensile Elongation Tensile Density
Karkkainen et al. [19] and Mallikarachchi et al. [20] proved that
strength [%] modulus [g/cm3]
[MPa] [GPa] under in-plane loading conditions, Tsai–Wu failure criterion can
properly describe the failure of the woven composite. Thus,
Carbon TC33 3450 1.5 230 1.8
fiber Tsai–Wu failure criterion is implemented in the present study.
Matrix LY1564/ 70–80 4.0–5.0 3.0–3.2 1.0–1.1 The quadratic polynomial Tsai–Wu failure criterion under
Aradur3486 in-plane loading in stress form can be described as [21],
632 Z. Liu et al. / Composite Structures 140 (2016) 630–643
Table 2
Mechanical properties of the carbon fiber woven composite.
Fig. 2. Schematic illustration of experimental and numerical results of three point bending test.
(a) Drop weight impact test (b) Numerical simulation Fig. 6. The profile of the original bumper.
(d) Foam
Fig. 7. The integrated bumper system: (a) bumper beam system; (b) bumper beam; (c) towing hook component; (d) foam.
Five thickness variables and four shape variables are selected as parts of the tow hook component are modeled by shell element
optimization inputs shown in Fig. 9. Variables X1, X2, X3, X4 and X5 except the socket with hexahedral element and all the element
are the thickness of the corresponding areas and will be considered sizes are 5 mm. Different components are tied together in a static
in the optimization procedure. For the impact process, energy simulation. While in impact simulation, surface to surface tiebreak
absorption is the area under the force displacement curve, which contact is defined to simulate the detachment behavior between
is proportional to the force and the crush length. Therefore, shape the foam and the bumper.
variables X6 and X7, which represent the crush length, are consid- The detailed material properties have been characterized in
ered in the optimization design procedure. It is widely recognized Section 2, and the simulation model is established based on classi-
that the transition fillets illustrate relatively strong effect on the cal lamination theory. Each of the ply is 0.25 mm. In the present
energy absorption process and deformation pattern of the bumper study, the stacking sequence has not been taken into account in
beam. Hence, radius variables X8 and X9 are brought into the the optimization problem, and 45° plies have been added into
design procedure. the laminates to balance the mechanical performance. The lami-
nates are assumed to be symmetric and the sequence is
3.2. Finite element modeling [02/452/0n/452/02]. Fig. 11 is the schematic diagram of an 11-plys
carbon fiber composite material.
The geometry modification procedure is conducted in the com-
mercial code CATIA. HyperWoks is applied to generate the finite 3.3. Finite element simulation
element model of the bumper system due to its excellent perfor-
mance in mesh generation (see Fig. 10). Since the average thick- In this research, strength analyses of the tow hook block, low
ness of the bumper beam is much smaller than the other velocity impact simulations and noise vibration and harshness
dimensions, shell element is the best modeling type and its size (NVH) are taken into consideration.
is chosen as 5 mm. Considering the anisotropic properties of the The strength analysis is performed using implicit computing in
carbon fiber composite, the bumper beam is divided into 25 parts ABAQUS. The simulation model is shown in Fig. 12. A part of the
for attaching local coordinate systems. The foam is simulated by front rail is included in the model, which is fully constrained at
tetrahedron elements with 5 mm mesh size, and MAT57 (⁄MAT_L the end during the static analysis. The loading force applied on
OW_DENSITY_FOAM) is used to model its material behavior. The the tow hook is 50% of the gross vehicle weight (GVW). There
Z. Liu et al. / Composite Structures 140 (2016) 630–643 635
are six load cases as shown in Table 5. Load cases 1 and 4 simu- and the barrier should not be deformable. Fig. 14 illustrates the
late the tension and compression conditions of the tow hook. simulation model.
Load cases 2, 3, 5 and 6 represent the conditions when the tow The bumper’s NVH property is computed in ABAQUS and the
hook is loaded at certain angles. Stress results must not exceed value of the first-order mode frequency must be more than 25 Hz.
the strength limit of the composite material with predefined
safety factor. 4. Optimization procedure and results verification
The impact behavior of the bumper system is checked according
to the conditions stated in E.C.E., Regulation No. 42, 1994 [26] and As mentioned above, many load cases should be considered in
RCAR (Research Council For Automobile Repairs) regulation [27]. the design process of the bumper system. In this research, static
Low velocity impact simulations are conducted using Ls-Dyna. strength analyses and dynamic impact simulations are combined
For E.C.E. standard, the impactor is a steel structure modeled by together to conduct the structural optimization procedure. A tech-
rigid solid elements. The impact velocity is 4.25 km/h and Fig. 13 nological methodology for the design of composite bumper beam
shows the straight (perpendicular) impact situation. from geometrical modification to structural optimization is pro-
Impact point is located in the 40% width of the vehicle frontal posed with the application of Kriging modeling technique and a
structure at the driver’s side. The test velocity is set to 15 km/h modified PSO optimizer, which will be clarified thereinafter.
636 Z. Liu et al. / Composite Structures 140 (2016) 630–643
X-Z Plane
where r
^ 2 is a function of hk and pk :
^ R1 ðY F bÞ=n
r^ 2 ¼ ðY F bÞ
T
^ s ð11Þ
2
The R criterion is used to assess the accuracy of metamodels
shown in Eq. (12). Where y i is the mean response value of test
^i is the predicted response value and yi is the real test
points, y
response value.
Pntest
^i y
ðy i Þ2
R2 ¼ Pi¼1 ð12Þ
ntest
2
i¼1 ðyi yi Þ
^ ^ þ rðxÞT R1 ðY F bÞ
^
YðxÞ ¼b ð8Þ xikþ1 ¼ xik þ v ikþ1 ð15Þ
where Y is the exact system responses; F is a unit matrix; elements
^ is estimated ðiter max iterÞ
in rðxÞ are correlation function Rðx; xi Þði ¼ 1; . . . ; ns Þ; b xðiterÞ ¼ ðxmax xmin Þ þ xmin ð16Þ
using least squares regression: itermax
638 Z. Liu et al. / Composite Structures 140 (2016) 630–643
Table 6
Load cases description of the bumper system.
Eq. (14) is the velocity update equation. Its first part is the initial cognitive scaling parameter and c2 is social scaling parameter
velocity with inertia factor x which provides momentum for par- [38]. r 1 and r 2 are two uniformly distributed random numbers
ticles moving across the design space and is also used to balance within the range [0, 1].
the global and local search abilities during the optimization pro- The movement of particles in the PSO algorithm can result in a
cess [35]. Shi and Eberhart [36] have proposed a linearly varying fast convergence rate, but it will lead to premature convergence
inertia weight which had a significant improvement in the perfor- problem because of a quick loss of diversity, which interprets the
mance of the standard PSO, as shown in Eq. (16), in which iter rep- degree of dispersion among particles [39–41]. At the beginning of
resents the current generation and itermax is the maximum the optimization procedure using PSO, the diversity of the particle
generation number. The second part of Eq. (14) is named cognition swarm is high after initialization. Along with the proceeding of
component which represents the personal behavior of a particle evolution, the diversity is declined for the convergence of particles,
and encourages each particle to move toward its own best previous which strengthens exploitation (local search) ability but weakens
position. The third part is called social component which stands for exploration (global search) capacity of the algorithm. This process
the cooperation behaviors among particles [37]. c1 is named as is necessary at the early or middle stage of the optimization
Z. Liu et al. / Composite Structures 140 (2016) 630–643 639
Table 7
Kriging modeling details of multi-working conditions.
Table 9
Values of variables after the optimization procedure.
X1 X2 X3 X4 X5 X6 X7 X8 X9
Mathematical values 4.78 5.91 3.54 2.89 2.41 36.60 52.20 50.00 22.00
Practical values 5.00 6.00 3.50 3.00 2.50 36.60 52.20 50.00 22.00
640 Z. Liu et al. / Composite Structures 140 (2016) 630–643
Table 10
Finite element analysis verification.
adaptive reset operator while a small value will reduce the (4) In this step, the adaptive reset operator is activated. A prob-
computational efficiency. According to empirical observa- ability P is given here to decide when the velocities and posi-
tions, Gstagnation is set to 5 in this article [44]. tions of particles shall be reset. It is similar to the mutation
Z. Liu et al. / Composite Structures 140 (2016) 630–643 641
Fig. 17. The plastic strain of RCAR. Fig. 18. The impact force of RCAR.
642 Z. Liu et al. / Composite Structures 140 (2016) 630–643
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