112

CHAPTER 5

FINITE ELEMENT ANALYSIS OF THE BUMPER BEAM

The main purpose of bumper is to absorb shock in case of a

collision. Several materials have been used to develop these shock-absorbing

capabilities, such as steel, aluminium, glass mat thermoplastics and sheet

molding compound. The purpose of this project is to design a bumper which

is to improve crashworthiness of the bumper beam. Crashworthiness is the

ability of the bumper beam to prevent occupant injuries in the event of an

accident and this is achieved by minimizing the impact force during the

collision.

5.1 STRATEGIC PARAMETERS

The need for computer crash simulations with high degrees of

fidelity and robustness is becoming increasingly important for use in

parametric studies and early design analysis. The numerical simulations also

enable new design concepts to be evaluated where there is a need to establish

an optimum design with interaction between materials and structural forms.

The main objective of this chapter is to investigate the ability of the non-

linear FE code LS-DYNA (Hallquist 2003) to predict the response of the

bumper beam system. The main focus is placed on accurate prediction of the

observed system behaviour with respect to force-deformation characteristics

and fracture modes.

113

There were four main strategic parameters being studied during the

test modelling. In the first step for metallic material it was necessary to know

the type of material can affect the impact specifications and what kind of

materials could be used as replacement in order to lower part weights. The

effect of module of elasticity and yield strength on impact behavior of bumper

beam was under investigation in this section. Secondly, the thickness, i.e.,

how the bumper beams thickness could affect the impact specifications.

Thirdly, the shape, i.e., how could small changes and modifications result in

easier manufacturing processes and lessening material volume without

lowering the impact strength. Finally, the impact condition, i.e., how the test

conditions other than the previously mentioned parameters could affect the

impact behaviour.

Steel and Aluminium structures with a specified thickness that did

not fail during the test depicted clearly that they are not suitable as bumper

beam structure due to increased weight. They increased the weight of the

structure by nearly 500% and 100%, respectively, in comparison with

composite bumper.

In the next step, the composite materials like GMT,LFRT and

KLFRT were used and studied to find the best impact behaviour. Here

KLFRT material was chosen for its outstanding results in mechanical and

thermal properties. The summarize, the objective of this research was to

develop and propose a natual fiber composite bumper, which could satisfy

following requirements:

1. Easy to manufacture by the shape. This was accomplished by

removing strengthening ribs of bumper.

2. Being economical by utilizing low-cost composite materials.

114

3. Achieving reduced weight compared to the metallic bumper.

4. Achieving improved or similar impact behavior compared to

the currently used metallic structure.

5.2 MECHANICAL PROPERTIES OF MATERIALS

Mechanical properties for the bumper materials are given below in

Table 5.1.The values of Steel, Aluminium, GMT and LFRT were taken from

literature review (Mahmood et al 2008) the KLFRT composite values were

taken from the graphs drawn for tensile and flexural testing.

Table 5.1 Mechanical properties of the bumper materials

Material

Young’s

modulus

(GPa)

Poisson

ratio

Yield

strength

(MPa)

Density

(kg/m3)

Steel 210 0.3 700 7850

Aluminium 70 0.33 480 2710

GMT 12 0.41 230 1280

LFRT 9 0.45 190 1200

KLFRT 8.5 0.42 220 1240

5.3 COMMON REINFORCING BUMPER BEAM CROSS

SECTION

The bumper cross section plays very important role in designing of

the bumper beam. The cross section area of the bumper has direct contact

with the impactor.The cross section decides the energy absorption of the

bumper materials.

115

Figure5.1 Different cross sections of the bumper beam

The above Figure 5.1 Shows the different cross sections of the

bumper beams used in the passenger car.

5.4 LS DYNA FOR BUMPER TESTING

LS-DYNA is an advanced general-purpose metaphysics simulation

software package that is actively developed by the Livemore Software

116

Technology Corporation (LSTC). While the package continues to contain

more and more possibilities for the calculation of many complex, real world

problem, its origins and core-competency lie in highly nonlinear transient

dynamic Finite Element Analysis (FEA) using explicit time integration.

LS-DYNA is being used by the automobile, aerospace, construction, military,

manufacturing and bioengineering industries.

LS-DYNA is widely used by the automotive industry to analyze

vehicle designs. LS-DYNA accurately predicts a car’s behaviour in a

collision and the effects of the collision upon the car’s occupants. With

LS-DYNA automotive companies and their suppliers can test car designs

without having to tool or experimentally test a prototype, thus saving time

and expense.

A crash simulation is a virtual recreation of a destructive crash test

of a car using a computer simulation in order to examine the level of safety of

the car and its occupants. Crash simulations are used by automakers during

Computer-Aided Engineering (CAE) analysis for the crashworthiness in the

Computer-Aided Design (CAD) process of modelling new cars. During a

crash simulation, the kinetic energy, energy of motion, that a vehicle has

before the impact is transferred into deformation energy, mostly by plastic

deformation (plasticity) of the car body material (Body in White), at the end

of the impact.

Data obtained from a crash simulation indicate the capacity of the

car body structure to protect the occupants during a collision (and also

pedestrians hit by a car) against injury. Important results are the deformations

(for example, steering wheel intrusions) of the occupant space (driver,

passenger) and the decelerations (for example, head acceleration) felt by

them, which must fall below threshold values fixed in legal car safety

regulations. To model real crash tests, today’s crash simulations include

117

virtual models of crash test dummies and passive safety devices (seat belts,

airbags, shock absorbing dash boards.etc.).

Thus the basic concept of the existing bumper systems, the type of

materials and the effect of different cross section used in bumper system were

studied. Software required for modelling, meshing and analyzing the bumper

beam such as Hypermesh and LS Dyna were utilised.

5.4.1 Explicit Simulations

Only explicit crash simulations were performed in this study.

However, implicit dynamic simulations of the bumper beam-longitudinal

system can also be performed but the convergence becomes critical due to the

number of contact definitions, which requires lot of simulation time (Kokkula

et al 2003). The simulations were performed on a single Linux processor.

LSDYNA uses a central difference operator for time integration, requiring a

limitation on the time-step size. To obtain numerical stability during the crash

simulations, the time-step size is typically in the order of one microsecond.

All the simulations were executed with a variable time-step. It is also possible

to execute the simulations with a fixed time-step, which generally has the

potential of yielding large errors in analyses including inertia effect.

5.5 DEVELOPMENT OF BUMPER BEAM FOR THE FEA

SIMULATIONS

5.5.1 Specification of the bumper

As initially a chosen passenger car bumper beam in analysis.

Material used in bumper beam- steel

Outside to outside - 1070mm

118

Height - 125mm

Between supports - 950mm

Thickness - 2mm

Cross section of the beam - Hat

5.5.2 Modelling

The accuracy of any simulation depends on how accurately the

modellingr work has been carried out. The Modelling of the bumper beam is

done by PRO-E modelling software using the above mentioned dimensions.

Firstly modelling the Hat section followed by C, Double Hat and Hot Box

section were done.

Hat section

The below Figure 5.2 shows the PRO-E model of the Hat section

bumper beam.

Figure 5.2 Hat section

119

C section

The below Figure 5.3 shows the PRO-E model of the C section

bumper beam.

Figure5.3 C section

Double Hat section

The belowFigure5.4 shows the PRO-E model of the Double Hat

section bumper beam.

Figure 5.4 Double hat section

120

Hot Box section

The belowFigure5.5 shows the PRO-E model of the Hat section

bumper beam. Efforts were taken in constructing the model of the bumper

beam as similar as possible to the reality. The bumper beam and all other

components in the system was modelled and meshed in order to make a

precise model using PRO E and HYPER MESH. Thus the dimensions of the

bumper used in the passenger car were measured and using the PRO-E

software the model of the bumper beam was designed for the different cross

section.

Figure 5.5 Hot box section

5.6 DEVELOPMENT OF FEA MODEL FOR THE BUMPER

BEAMS

5.6.1 Meshing

The conventional model which was developed in PRO-E software

has to be meshed for analysis of crash. For this HYPERMESH software is

used. Altair Hypermesh is a high-performance finite element pre-processor

that provides a highly interactive and visual environment to analyze product

121

design performance. With the broadest set of direct interfaces to commercial

CAD and CAE systems, Hypermesh provides a proven, consistent analysis

platform.

Steps involved in meshing.

Geometric cleanup.

Taking mid surface.

Rough mesh and Quality check.

Applying contact elements.

Rigid surface for crashing.

Creating control card for crash.

Exporting the FEA model to LS DYNA software.

Process involved in exporting the meshed model to LS DYNA.

Checking connectivity.

Checking the connectivity between elements.

Combining nodes of every structure.

Impact area definition.

Development of rigid area.

Material selection for rigid element.

Creating of rigid impact barrier.

Creating contact card.

Surface to surface contact has to be defined.

Defining master and slave contact cards.

122

Defining AUTOMOTIVE option.

Velocity of contact cards has to be defined.

Velocity of particular nodes has to be mentioned.

Control Energy Development.

To obey cube rebound theory.

Shell element and solid element internal energy definition.

Defining Control output.

Result frequency has to be defined.

Control termination.

Defining end time of the impact or process.

Number of cycles to be defined.

5.6.2 Boundary Conditions

The below Figure5.6 shows the boundary conditions of the bumper

beam in Hypermesh software.

Figure5.6 Meshedmodel of bumper and impactor

123

The gap between the impactor and bumper beam is 50mm.

Bumper beam - MAT24 PIECEWISE_LINEAR_PLASTICITY

Impactor - MAT 20 RIGID MATERIALS

Mesh element size -10

Each side 10 elements are constrained i.e., all degrees of freedom

were arrested.

The meshed model is imported to LS DYNA software for crash

analysis. The conditions are

Velocity of the impact barrier was 48 kmph for FMVS standard and

68 kmph for IIHS standard.

Crash type : frontal impact.

Obstruction : rigid barrier.

Simulation time : 12 ms.

The bumper beam will have some residual stresses because of the

stretch bending operation; these stresses will try to relax elastically, when the

stretch-bending tools are removed, to reach an equilibrium state. The elastic

recovery of stresses corresponds to an unloading phase; in general implicit

codes are more effective to represent this phase, see Mercer et al

(1995).Hence, an implicit spring back simulation was performed. The spring

back analysis was performed on the dynain1file obtained at the end of stretch

bending operation. It was observed from the simulation that there was a

shortening along the length of the bumper beam in the axial direction Thus

the model created in PRO-E were into Hypermesh, using mesh tool the

models were fine meshed and input parameters for the analysis the bumper

beam were given and run using LS Dyna software.

124

5.7 DEVELOPMENT OF MATHEMATICAL MODEL FOR THE

FRONTAL IMPACT

The simulation results which has been developed has to be

validated. But the experimental tests are very expensive and time consuming

to do a detailed work on this project. So there are some other ways to validate

the model.An alternate way to achieve the proposed result is to develop a

numerical model for the bumper and pendulum system for frontal collisions.

5.7.1 Quasi- Static Impact

Perhaps one of the most fundamental questions regarding the

analysis of this type of impact is whether transient, dynamic analysis is

necessary. The previous test experience discussed here suggests at non-linear

material and geometric behaviour is significant. If transient dynamic defects

also must be included also, the analysis should be very burdensome. To assess

this issue, some simple spring-mass models were employed.

The first model considered with regards to these basic questions is

shown in Figure 5.6.The pendulum is modeled simply as a rigid solid of mass

M with an initial velocity of V. Otherwise, the car is modeled as a rigid solid

of equivalent mass M. However, the stiffness of the bumper beam is included

in the model as a spring of stiffness K. This stiffness can be identified either

experimentally or analytically. From the mechanics of materials, the stiffness

of the beam is K= 48EI/L³ when the external loads applied on its center. Here

the E is the Young’s modulus of the materials, I is the moment of inertia and

L the total length of the bumper beam.

125

Figure 5.7 Equivalent spring mass system for bumper and impactor

The validation of the FEA analysis of the bumper testing is

essential ,it is necessary to redefine and check the values before the prototype

of the bumper design.To optimise the FEA results this numerical modelling

was developed and to help to compare the values. The impact behavior in

vehicle collision is assumed as shown in Figure 5.7 this type of vehicle

collision is named as elasto-plastic impact (Nimmar et al 1987). During low

speed impact, the collision involves transient and non-linear analysis. To

assess this issue some simple spring-mass model was employed. Here the

pendulum is modeled simply as a rigid solid of mass M with an initial

velocity of V. Similarly, the car is modeled as a rigid solid of equivalent

mass M. Since the mass of the bumper is small with respect to the car, it is

neglected in this analysis. However, the stiffness of the bumper is included in

the model as a spring of stiffness KB. This stiffness can be quantified either

experimentally or analytically by considering the displacement ‘y’ of a

bumper beam under a load F from a pendulum. Then the stiffness KB simply

becomes

y

F

Deflection

LoadKB (5.1)

126

The governing differential equations for the dynamic system

described in Figure 5.7 are

0)( 211 xxKxM B (5.2)

0)( 212 xxKxM B (5.3)

and the initial conditions are

0)0(1x (5.4)

Vx )0(1 (5.5)

0)0(2x (5.6)

0)0(2x (5.7)

Solution of this set of simultaneous linear equations leads to

tV

tV

x 2sin222

1(5.8)

tV

tV

x 2sin222

2(5.9)

where t and stands for time and angular velocity respectively,

M

KB (5.10)

A number of very important conclusions can be drawn from

Equations (5.8) and (5.9). An expression for the total force exerted by the

pendulum on the bumper for Equation (5.11) can be derived as

127

2t (5.11)

)( 21 xxKF B (5.12)

tMK

VF B 2sin2

(5.13)

2max

MKVF B (5.14)

In addition, the impact event terminates when the force goes to zero

and that “Total impact duration, S” can be expressed from Equation (5.13).

2S (5.15)

The information contained in Equations (5.14) and (5.15) is

important from a number of standpoints. The Equation (5.14) defines a

structural load in terms of the mass and velocity of the pendulum. Such loads

are necessary for the application of detailed finite element analyses.

Furthermore, the variation of this structural load can now be clearly defined

for different impact velocities and automobile masses. This is essential for the

consideration of impact response at different velocities and design for

application on automobiles of varying sizes. As the impact event takes place,

the pendulum velocity gradually decreases from V to 0 while the automobile

velocity increases.

As a result the bumper does not absorb all the kinetic energy of the

pendulum. Instead, some of the kinetic energy is transferred to kinetic energy

of the car. The “Maximum energy absorbed, U” by the bumper during the

impact can be defined as

128

2

max21 ])[(2

1xxKU B

(5.16)

22

max

4

1

2

1MV

K

FU

B

(5.17)

The principle of energy conservation in elastic impact is used; the

kinetic energy before impact is conserved and converted to elastic energy and

the kinetic energy of the impactor and the automobile at its maximum

deflection, i.e.,

2

2

2

2

2

max21

2

12

1

2

1])[(

2

1

2

1MVmVxxKmV B

(5.18)

Finally the KB is the spring constant of the beam,

3

48

L

EIKB (5.19)

5.8 DISPLACEMENT RESULTS

Table 5.2 shows the Displacement of different cross sections of the

bumper beam during the frontal collision Simulations. C cross section shows

excellent deformation compared to the other type of cross sections similarly

KLFRT material bumper beam gets more displacement compared with the

other cross section and other conventional material bumper beams during the

collision.

129

Table 5.2 Displacement Results of the bumper materials

MaterialsDisplacements (mm)

C Double hat Hat Hot box

Steel 240 265 260 269

Aluminium 252 268 271 267.5

GMT 270 267 262 267.7

LFRT 280 275 271 273.4

KLFRT 274 270 268 267

5.9 IMPACT FORCE RESULTS

Table 5.3 shows the Impact forces of the different cross sections of

the bumper beam during the collisions. C cross section with KLFRT material

bumper beam gets minimum impact force compared with the other cross

section and other conventional material bumper beams during the collision.

Table 5.3 Impact force results for the bumper beams

MaterialsImpact force (kN)

C Double hat Hat Hot box

Steel 57.15 62 58.76 70.9

Aluminium 25.44 21.23 22.25 27.45

GMT 11.11 16 13.2 13

LFRT 7.24 11 9 10.5

KLFRT 7.23 10 8 10

130

5.10 ENERGY DISTRIBUTIONS

FEA simulations make it possible to understand how the energy has

been distributed in the system with the progress of deformation. The energy

distributions were taken from the LSDYNA by the usage of GLSTAT options

and the energy curves were analysed for bumper materials .

5.10.1 Steel Bumper

From the Figure 5.8(a-b) the energy distribution of the steel bumper

was analysed and conventional steel material showed good energy absorption

during collisions.

5.10.2 Aluminium Bumper

Similarly from the Figure 5.9(a-b)the energy distribution of the

aluminium was plotted.Even the light weighted aluminium bumps good and

stores more energy.

5. 10.3 LFRT Bumper

Figure 5.10 (a-b) and 5.11 (a-b) the energy absorption of the

thermoplastic bumper beams were studied and it has challenging energy

absorbing capacity equal to the conventional materials and having advantage

of the light weight compared to steel and aluminium.

131

(a) As per FMVSS

(b) As per IIHS

Figure 5.8 Energy distributions of steel bumpers

132

(a) As per FMVSS

(b) As per IIHS

Figure 5.9 Energy distributions of aluminium bumper

133

(a) As per FMVSS

(b) As per IIHS

Figure 5.10 Energy absorption of LFRT

134

5.10.4 KLFRT Bumper

Kinetic energy and linear momentum are conserved; this can be

clearly observed in above diagrams. As seen, the car begins to obtain kinetic

energy at the same time as the impactor loses it. The results revealed that for a

given amount of deformation the predicted energy absorbed by the natural

composite KLFRT was higher with the currently available material models in

LS-DYNA.

(a)FMVSS

(b)IIHS

Figure 5.11 Energy distributions of KLFRT bumper

135

Energy conservation time of Steel, Aluminium, GMT,LFRT and

KLFRT material according to the FMVS standard and also according to the

IIHS Standard are shown

in Figures 5.8 (a-b) to 5.11(a-b). From these graphs it was found that KLFRT

bumper had more kinetic energy from impactor transfer to the bumper within a

short time compare to other material bumper beam.

5.11 DISPLACEMENT Vs TIME

Comparison of the displacement with respect to time was plotted

for the various type of materials were plotted and the results were extracted

from LSDYNA, according to the FMVS Standard and IIHS standard.The

pendulum hits the bumper with 48km/h velocity and 64km/h. The deflection

is an important parameter to check the crashworthiness of the bumper beam

material from a comparison of the graphs, it becomes clear that the KLFRT

shows an increase in deflection. The deflection is directly proportional to

material stiffness and yield strength. So the KLFRT can replace the

conventional bumper materials.The maximum displacement of KLFRT was

61.2mm at 6.7ms as per FMVSS, 78.5mm at 6.2 ms as per IIHS.

From the Figure 5.12(a-b) we can conclude that KLFRT composite

has the minimum displacement compared to all the other materials besides

meeting the safety requirements of FMVSS standard and taking minimum

duration. To reach its maximum deflection In the simulations a progressive

folding mode developed in the impacted front collision. One can easily note

this from the oscillations of curves around a mean value, after the maximum

peak in the graphs. The figure clearly depict that the simulations terminated at

a deformation of about 120 mm. At this deformation the impact energy was

absorbed by the bumper beam system. This indicates that if the unacceptable

failure in the impacted had not prevailed, thelongitudinal might have

deformed progressively up to the deformation predicted in the simulations .

136

(a) Fmvs Standard

(b) IIHS Standard

Figure 5.12 Displacement vs time

137

5.12 IMPACT FORCE VS TIME

The bumper beam frontal impact obtained maximum permanent

deformation when the impactor was stopped, i.e. when all the impact energy

was absorbed. In the simulations the impact energy is converted to plastic

work by bending and stretching of the bumper beam as well as crushing the

longitudinal at the impacted end and also bending of the non-impacted

longitudinal. In the initial stage of crushing, the active longitudinal members

locally squeezes and the stretch-bent bumper beam starts to flatten so that the

upper and lower flanges of the bumper beam will experience compression and

tension, respectively.

The impact analysis between the pendulum and the frontal bumper

during low speed crash involves transient and non-linear conditions which

lead to an elasto-plastic impact. During this low speed crash, the bumper

system should not have any crash or failure to prove the FMVSS.. The impact

force calculation relates to deceleration of impactor due to the after effects of

the bumper and the car. The impactor was assumed to be rigid material and

the bumper beam was made of metallic and composite material. The

distribution of the impact load is irregular along the area of collision to get the

maximum deflection.

To compare the differences among impact forces, the impactor

inertia force plays major role. From the Figure 5.12 (a-b) the impact force for

GMT, LFRT and KLFRT is notable as these have the lowest value with a

slightly longer time interval due to low rigidity of the same. Comparing with

the conventional materials the thermoplastic materials give more absorption

of impact energy which leads to the safety of the vehicle.The results shows

that natural fiber composite bumper can reduce the impact of collision with

higher performance and can successfully replace Steel, Aluminum, GMT ,

SMC and LFRT. The impact duration for the natural fiber reinforced

composite was the shortest compared to Steel, Aluminum, GMT and SMC.

138

(a) FMVS standard

(b) IIHS Standard

Figure 5.13 Force vs time

-5

0

5

10

15

20

25

30

35

40

45

50

0 0.5 1 1.5 2 2.5

Fo

rce

(KN

)

Time (ms)

Steel

Aluminium

GMT

lfrt

KLFRT

139

The analysis work was completed with the existing car bumper

with the help of Hypermesh and LS DYNA software and the displacements

and impact forces were studied during the collision and it was concluded that

the computer model could correctly predict the reaction force in non-

destructive impact test and then testified through comparing the computer

results and theoretical evaluation.Figure 5.14 shows the comparisons of the

FEA and Calculated values using numerical modelling of impact force .The

results shows favarouble error percentage for FEA and Calculated values.

Figure 5.14 Comparison of calculated and simulated values of force

during impact

Good agreement was found between the calculated values and

simulations when using the user-defined material model like LSDYNA.

0

10

20

30

40

50

60

70

STEEL ALUMINIUM GMT LFRT KLFRT

Imp

act

Forc

e(K

N)

Material

FEA

CALCULATED

ERRER

140

The displacements of the bumper beam were studied and it clearly

depicts that as the C section with natural fiber composite bumper beam get

more deflection during the collision compare to the other conventional

material bumper beam.The impact forces of the bumper beam were studied

and it clearly depicts that as the C section with the natural fiber composite

bumper beam get minimum force during the collision compare to the other

conventional material bumper beam.

5.13 SUMMARY

In this chapter Finite element modellingr of the bumper testing

during frontal collision was performed according to FMVSS and IIHSS

standards.Initially the bumper specification was taken from standard

passenger car bumper beam and modelled using PRO -E software. Thus the

dimensions of the bumper used in the passenger were measured and using the

PRO-E software the model of the bumper beam was designed for the different

cross sections like C,hat section,double hat section and hot box section.the

materials used for bumpers were Steel,Aluminium,GMT,LFRT and KLFRT.

The natural fiber composite were included for checking of the

crashworthiness of the material as bumper beam. The modelling and meshing

were done by using hypermesh and the analysis was done by LS

DYNA.During the testing of the frontal impact the regulations were

considered for impact pendulum testing.From the results the C section beam

shows better energy absorption and good crashworthiness compared to the

other cross sections. Similarly, the materials were optimised for displacement

and impact force for which the KLFRT reacts good as like the other bumper

material.

141

The natural fiber composites were found to have good absorption

of energy during frontal collisions and better crashworthiness equal to the

conventional bumper materials.