Problem Set 1 EMA 4714 - Materials Selection
and Failure Analysis
In class, we have considered selection of materials for face plates of golf
clubs - the objective in mind by the designer is, among other things, to maximize
distance traveled by the ball from a given amount of energy input produced by
the swing. Two reference sources were considered, both involving product application
divisions of commercial concerns - Carpenter Technology and Liquid Metal Technologies.
Each bases material performance on different criteria for performance as well
as different material properties.
1. Explain, derive or otherwise defend the statement [Carpenter], “Assuming that the distance agolf ball is driven relates to the hardness and tensile strength of the face insert, more of the energy of the swing should be transferred to the ball with the two aerospace alloys.” ***************************************************************************
Any argument has to be based on your understanding of the process by which the ball acquires its velocity. For a review of the physics of conservation of momentum, impulse and the like, see:
[http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l1c.html]
As I understand it, the "energy of the swing" must be conserved - i.e. in order
for the ball to acquire kinetic energy, there will have to be energy loss by
the club in the form of loss in velocity, sound, heat, plastic deformation and,
so long as it persists, elastic strain energy. If momentum is to be conserved,
then any increase in the velocity of the ball must be balanced by a decrease
in the energy of the club. Whether that energy decrease results from a decrease
in velocity or mechanical strain or some combination of both will not change
the fact that will have to decrease.
2. Explain, derive or otherwise defend the statement [Carpenter, page 90, 2nd
paragraph up fromthe end of the page], “The three steels in the group
of four metals studied have approximately 70% higher stiffness or modulus of
elasticity than the Ti-6Al-4V alloy (Fig.3). Therefore, they are stiffer and
support a greater load. As a result, inserts of those high-modulus, high-strength
alloys will absorb less energy at the point of impact than titanium, and thus
transfer more energy to the ball.” ***************************************************************************
Stiffness is a term used to describe the force required to produce a given defection [in a beam], i.e. S = F/
, and appears to be the reciprocal of Compliance. In a sense, it is directly proportional to the modulus of elasticity, although beam length and its moment of inertia also contribute to S. When the Carpenter people claim the steels "support a greater load", they probably mean that under a given load, the steels undergo less elastic deformation. That being the case, the steels will unquestionably "absorb less [elastic] energy at the point [sic] of impact" [I question the use of the term "point of contact" since the ball surely flattens upon impact]. The fact that a stiffer club face absorbs less elastic energy does not, in my mind, mean that more energy is transferred to the ball.
According to the laws of physics [the referenced web site], as long as contact time between the ball and club is the same, force [load] experienced by both bodies will have to be the same - the only way to increase the momentum acquired by the ball for a given
applied load/force would be to increase the time of contact [impulse = F*t = m
v]. This
would seem to support the argument presented by the LiquidMetal people - that
increasing the compliance of the club results in increased ball velocity - not necessarily
because of reduced force being applied to the ball but because elastic deformation in the
club face results in the face molding around the ball during contact, thereby increasing the
contact time. It is interesting to note that, for better or worse, these clubs are known to
give increased elevation [lift] to the ball.
3. Explain, derive or otherwise defend the statement [Liquidmetal], “A
perfectly elastic sphere would show load being proportional to displacement
raised to the 3/2 power identically upon loading and unloading.” ************************************************************************************
As an elastic sphere deforms [flattens] upon contact
with a planar surface, the area of contact increases with respect to the amount
of displacement. In a sense, the applied force producing thedisplacement is
being distributed over a larger area, resulting in a decreased stress.
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