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Review of Literature
A push or pull upon an object resulting from the object’s interaction with another
object, a force is divided into two categories: contact and action-at-a-distance. Contact
forces result when two objects interact by physical contact. For instance, kicking a ball
involves contact force, because the ball makes physical contact with the kicker’s foot. On
the other hand, action-at-a-distance forces, known as “non-contact forces”, result when
two objects interact without physical contact. All four fundamental interactions--gravity,
electromagnetism, strong nuclear force, and weak nuclear force--are action-at-a-distance
forces (Henderson, Types of Forces). Of the many types of forces described, the research
concentrates on determining contact force.
In addition to force, there are two types of collisions: elastic and inelastic. A
perfectly elastic collision occurs where there is no loss in kinetic energy in the system
and momentum is conserved. An example of this is are two rubber balls colliding head
on. In an inelastic collision, momentum is also conserved, but some of the kinetic energy
is transformed into another type of energy. A good example of this is a head-on collision
between two cars because the kinetic energy transformed heat energy due to friction.
Nonetheless, no large scale collision is perfect: despite the collision, some of the kinetic
energy is always converted into internal energy, the energy in a system arising from the
relative positions and interactions of its parts. When two bodies collide, the velocity of
each object changes, which results in a change of each object’s momentum. Impulse, the
change in the momentum of an object, describes the effect of a net force that acts on an
object (Henderson, Momentum and Impulse Connection). According to Newton’s third
law, impulse is applied to one of the bodies to prevent interpenetration by applying an
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equal and opposite impulse to the other body (Henderson, Newton’s Third Law). The
impulse of a collision is calculated by multiplying the final velocity by the colliding
object’s mass and then subtracted by the initial velocity multiplied by the colliding
object’s mass. A crumple zone in the front and back of a car reduces the vehicle’s
velocity, its momentum, and the force exerted on the passenger compartment of a vehicle
by lengthening the time of a collision.
𝛥𝛥 = mvf - mvi
Figure 2. Impulse Formula
This is shown in Figure 2 in the form of an equation, where 𝛥𝛥 is impulse, 𝛥 is
the mass of the colliding object, and vf and vi are the final and initial velocities
respectively. However, impulse is not the only factor that determines a collision.
Although the purpose of the research is to determine which material absorbs the
most energy from an impact by calculating its force, there are other factors that determine
the collision between two objects. For instance, Basaraba-Opritescu’s and Toader’s 2007
research on the “Simulation Methods in the Contact with Impact of Rigid Bodies”
determines the collision between two objects by the processing of signals. One signal that
their research emphasizes is on the frequency of vibrations. Depending on the amount of
force, whenever a “perturbing force” acts on an object, the object tends to vibrate. Using
an ANSYS LS-DYNA program, which simulates the response of materials to shortduration severe loading, Basaraba-Opritescu and Toader discovers that elasticity
positively correlates with frequency (Hz). Rigid bodies with an elasticity level of ten had
a frequency of approximately 987.52 Hz, while those with a level of twenty-four had a
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frequency of approximately 14,177.46 Hz (Basaraba-Opritescu, Cristina, and Toader).
Seen that an object with a greater ability to resume its normal shape after being
compressed will ultimately have a greater frequency, this is mathematically proven by
dividing the stress (the force per unit area applied to the material) of an object by its
strain (relative change in shape or size implies that it is dimensionless and has no units)
(“Stress & Strain”). The results from this experiment led to the researchers to hypothesize
that the polycarbonate plastic would absorb the greatest amount of force due to its
elasticity.
Figure 3. Logger Pro Software
While an object’s elasticity and vibration frequency can be used to determine the
force of an impact as seen in Toader’s research, Logger Pro software and LabQuest
technology offers a simpler, more cost-effective alternative. The Logger Pro software is
show above measuring the force of an impact over time. With a “force plate”--measuring
instruments that measure the ground reaction forces generated by a body moving across
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them--Logger Pro and LabQuest can calculate force of an impact with the click of a few
menu selections (Figure 3). Not only does the program make it easier to obtain the force:
the impulse can be found by locating the time frame in which the force of the impact
suddenly rises to its peak. This does not mean, however, that elasticity and frequency of
vibrations should be ignored in the research. In terms of elasticity, polycarbonate plastic
is less likely to relatively change in shape or size than both aluminum and steel. While
the average yield strain for aluminum and steel is approximately between 240 and 290
N/mm2 (respectively), the average yield strain of polycarbonate plastic is less than 100
N/mm2 (Höglund, Soetens, Rothe, Hirsch, Ryckeboer, Lundberg, AluMATTER |
Aluminium | Overview | Aluminium v Steel: Stress-Strain Behaviour). Greater strain (and
stress) increases the elasticity of an object, making it much easier for the object to absorb
the forces of impact.
As previously mentioned, there are various materials used to build vehicle
bumpers; most frequently used are polycarbonates, polyesters, and polypropylene.
Various materials are used to build vehicle bumpers, instead of only one, because design,
cost, and other factors come into play. Kumar, Belagali, and Bhaskar ran a comparative
study of automotive bumper with different materials for passenger and pedestrian safety
in 2014 stating that composite bumpers should be easy to manufacture, economical,
lightweight, and have improved and similar impact behavior.
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Figure 4. Dimensions of Bumper (from Kumar, Belagali, Bhusker)
Recall that design is important to a vehicle’s crumple zone: design parameters
such as cross section, longitudinal curvature, fixing method, rib thickness, and strength
play a significant role, as dimensions such as curvature radius, stay span length, and
sectional area are used to calculate the compressive strength, tensile strength, and the
strength-to-weight ratio (Figure 4) (Kumar, Belagali, and Bhaskar). The researchers of
this experiment used rectangular sheets of aluminum, steel, and polycarbonate plastic
instead of samples with unique designs because they believed giving each material a
different design may affect the result of the bumper. Again, the purpose of the experiment
is to determine which material absorbs the most energy from an impact; the researchers
meant to generally apply this to all vehicles. Despite this, the design of aluminum, steel,
and polycarbonate plastic themselves may be a factor to determining the force of an
impact and perhaps what material is an effective alternative to the contemporary bumper.
Kumar, Belagali, and Bhaskar concluded that carbon fiber was most effective in ensuring
pedestrian safety due to its light weight, durability, and ability to handle more stress and
strain. In terms of the research, the polycarbonate plastic design is partially responsible
for its greatest elasticity of the three materials. Its light weight and ability to stretch with
less strain absorbs more energy in a force of impact. While the design of the bumper
itself is not necessary to determine the force of impact in this experiment, the design of
the material, in which weight and thickness is applied, is important to determining the
force of impact in a collision.
Overall, the purpose of this research is to determine which material--steel,
aluminum, or polycarbonate plastic--absorbs the force of an impact the most.
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Polycarbonate plastic was predicted to absorb the most force in a collision. The force of
impact, momentum of the colliding object, impulse, material, and design are several
factors that determine a collision. Many vehicle bumper materials commonly contain
polycarbonates, polyesters, and polypropylene along with chrome or steel on many older
vehicles and pickup trucks. These materials have different results regarding the amount
of force absorbed in a collision. Ever since the invention of the automobile, there have
been thousands of technological innovations that have improved its safety for our use.
The safety of our vehicles is paramount to our own, as they are a common necessity for
our everyday transportation.