Materials Selection Lab Report

Transcription

1 Roman Kyrychenko Page 1 of 8 Student Number: Lab Practical Section: 0104 Materials Selection Lab Report by Roman Kyrychenko Faculty of Applied Science and Engineering University of Toronto Unsupervised Term Work Statement I hereby certify that I am thoroughly familiar with the contents of this laboratory report: it is substantially my own work, I have referenced all my sources of information, and I am the sole author. Type name here: Roman Kyrychenko Date: December 9, 2009

2 Roman Kyrychenko Page 2 of 8 Abstract This report explores the shortcomings of wooden sticks and, through an examination of the fracture dynamics of wood and the requirements of hockey players, suggests alternative materials that could improve various aspects of hockey sticks performance. To accomplish this, the Material Performance Indices (MPI) were derived for hockey sticks and CES software was used to graphically display the materials that maximize the MPI. In other words, materials were chosen to meet a number of objectives, including strength (with a certain amount of flexibility), light weight, and resistance to everyday wear and tear. Introduction For this lab, I will investigate the breaking of a wooden Sherwood PMP7000 hockey stick and examine how its structural properties, or rather those that affect its performance, could potentially be improved by changing its material composition. I chose this specific model because it is (unofficially) considered to be one of the most powerful and durable hockey sticks, being used for years mid 1980 s to the mid 1990 s by the National Hockey League s (NHL) most elite players. Al MacInnis, six-time winner of the hardest shot competition 1, used this stick for a large portion of his professional career, even when most NHL players changed their preferred sticks to composite, primarily Kevlar and carbon fiber designs. The primary reason for this shift was a need to make sticks that last longer 2, and shoot harder, but many players and coaches have had concerns that composite sticks do not last any longer than wooden ones, cost far more money ($150 apiece versus $30). More importantly (at the professional level), composite sticks often break suddenly and at the wrong times. Boston University hockey coach Jack Parker claims that, with a wooden stick, a player can tell when it's about to break and goes to the bench for another. With a composite stick, it's a sudden explosion 2. So, in this lab, I will explore the shortcomings of wooden sticks their apparent brittleness and proneness to warping and how they could potentially be addressed with a change in materials that would also avoid the aforementioned pitfalls of composite sticks. Most wooden sticks are made with layers of high-quality plywood sandwiched between layers of resin or fiberglass, making them cheap and easy to manufacture, but also not very well suited to absorbing large amounts of energy in a very short period of time, as in during a slapshot. Since slapshots are by far the most common reason for sticks breaking, stick failure will be examined and the subsequent recommendation of

3 Roman Kyrychenko Page 3 of 8 potentially superior materials will be made so that the new stick would withstand repeated slapshots without permanent deformation. Description of Failure The primary goal of a hockey stick is to maximize the transfer of kinetic energy from the player (related to the moment around the hand at the top of the stick) to the puck. In a slapshot, a player hits the ice a few inches behind the puck in order to elastically deform the stick and release the stored energy to propel the puck forward. This means that a hockey stick needs to be designed with a certain amount of flexibility, and this flex value ranges from 50 to 110 for most sticks. These values refer to the amount of downward force in pounds, which needs to be applied at the center of the shaft to deform the stick one inch. Thus, a flex of 100 would mean that 100 pounds of force are required to deflect the stick one inch in a 3-point-bend test. It is important to understand that the kinetic energy delivered by the stick to the puck is at a maximum when the stick is deformed elastically just before it reaches its yield stress. However, a stick that flexes too much will lead to inadequate control of the puck. Thus, this compromise determines the ideal choice of stick for a player. Since this ideal is obviously subjective and impossible to accurately incorporate into the calculations for the Materials Performance Index (MPI), a constraint on the magnitude of flex needs to be set when evaluating potential materials (this will be discussed in the next section). Looking at Figure 1,

4 Roman Kyrychenko Page 4 of 8 Figure 1: Sherwood PMP7000 under load of slapshot. we can see that the stick bends around the player s bottom hand, and a slapshot is effectively a 3-point-bend test around that point (we assume this is the midpoint of the shaft). Thus, this is the point at which a brittle failure occurs. According to a test performed by exploratorium.edu, it took nearly one ton of force 3 (just under 2000 pounds or 8907 Newtons) to break a typical new wooden stick (see Figure 2 on next page) and, since sticks break quite often, one would need to maximize this amount in order to increase durability. Figure 2: Hockey test snapped in lab through bending. Though the consequences of a brittle failure can hardly be called life threatening, even though snapped sticks have hit other players in the face after failing and flying off, the cost of a failure may be quite high. Of course, a stick can always snap at the wrong time, temporarily taking the player out of the game to give the opposing team an advantage and, in the case. For a wooden stick, this would not be an expensive failure, as a new one usually costs less than $40. Analysis of Original Design As mentioned before, the Sherwood PMP7000 design incorporates interconnected layers of highstrength plywood and fibreglass. Though the exact specifications for this stick could not be found, comparable sticks use a 22-ply construction, which would increase strength and reduce the stick s proneness to splintering and warping due to varying temperatures and applied pressure. The other major factor affecting the performance of a hockey stick is mass; a reduction in mass allows the player to increase the kinetic energy of his shot through an increase in velocity. Since the outer dimensions of wooden hockey sticks are fixed, a lower material density

5 Roman Kyrychenko Page 5 of 8 would equal lower mass. Thus, a strong and stiff yet not dense material is required for construction. While cost is a major factor in the vast majority of design processes, it can be disregarded in a few given cases; while the cost of a hockey stick is definitely relevant for amateur and recreational players, it is not a concern for professional ones. So we can derive the MPI values based on the stiffness vs. density and strength vs. density relationships. Stiff light beam (with derivation): Minimize mass: m = A L ρ Constrain stiffness: δ= FL 3 / C 1 EI I = f (A 2 ) δ= FL 3 / C 2 EA 2 Free variable: rearrange constraint equation: A = (FL 3 /C 2 Eδ)^(1/2) Performance function: constraint into objective, rearrange to FGM: m=[(fl 3 /C 2 Eδ)^(1/2)] L ρ m=[(f/c 2 δ)^(1/2)] [L^(5/2)] [ ρ/e^(1/2)] Material Performance Index: M= [E^(1/2)] / ρ Strong Light Beam: Material Performance Index: M= [σ^(2/3)] / ρ Evaluation of Original Design and Alternatives To turn the MPIs into values to graph using the CES software, we take the logarithms of both sides. M= [E^(1/2)] / ρ M= [σ^(2/3)] / ρ Log (M) = log ((E^(1/2)) - log (ρ) Log (M) = log ((σ^(2/3)) - log (ρ) ½ log (E) = log (ρ) + log (M) 2/3 log (σ) = log (ρ) + log (M) Log (E) = 2 log (ρ) + 2log (M) log (σ) = 3/2 log (ρ) + 3/2 log (M)

6 Roman Kyrychenko Page 6 of 8 To select the most appropriate materials, the line is moved upwards until only a few material groups remain above it (See Figures 3 and 4 on next page) Figure 3: MPI slope graph for a stiff light beam. Figure 4: MPI slope graph for a strong light beam.

7 Roman Kyrychenko Page 7 of 8 Recalling that it took almost 9KN of force to break a hockey stick, wood can be considered a satisfactory material for making hockey sticks; very few amateur players can exert sufficient force to break a stick. However, the CES graph implies that Rigid Polymer Foam (RPF) would be a better material, because of its low density and relatively high strength and Young s modulus, though since there have been no mass-produced sticks made out of RPF, it is difficult to judge how well the material would feel in the player s hands and how prone it is to warping and general wear and tear due to repeated use. Likewise, one can t know for sure how much elastic energy can be store in RPF. Yet another disadvantage is price; RPF costs 15.7 to 26.2 times more than wood per kilogram ( $/kg vs $/kg), a factor that more than offsets its low-density advantage. So, even though carbon fiber and Carbon Fiber Reinforced Plastics (CFRP) have disadvantages in terms of their high cost and unpredictable fracture patterns, their ability to transfer large amounts of energy as well as their light weight make them the best known material for hockey sticks, which would account for the vast majority of NHL players adopting these composite sticks over the past decade and a half. Conclusion In order to find the material that is best suited to a real life application, it is important to not only consider the design objectives, but also the compromises that result when one objective is seemingly at odds with others. Similarly, the relative importance of objectives is subjective to the user the hockey player, in this case and so it is very difficult to suit a mass produced design to the requirements of a specific user. For this reason, professional hockey players choose to have their sticks custom made to suit their playing style. To cater to recreational and amateur players, sports equipment companies offer sticks in a very wide variety of lengths, curves, weights, and flex ratings. References 1) John Ochwat, First Person Irregular: Hockey Analysis, Not Rocket Science [blog] (January 27, 2008) Available at HTTP: 2) B. Matson, Bit of a sticky situation, The Boston Globe, 29 Jan., pp. 1-2, ) Thomas Humphrey, Shooting the Puck Exploratorium.edu, (December 9, 2009) Available at HTTP:

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