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MSE 5090: Case Studies in Material Selection

Student Case Study Guidelines - Background Examples

Contents of this page:
 
Case Study: A look inside Snowboard Construction Components
Materials selection for a High Performance Ice Axe

Case Study: A look inside Snowboard Construction Components1

Background

The X freestyle boards that DNR produces for Santa Cruz have a three-ply laminate tip and tail. In the corners of the tip and tail of the snowboards, Santa Cruz has designed their boards to have a rubber piece as the middle ply. This rubber piece in the tip and tail corners allows for more give in transition, thus resulting in smoother take off and landings in freestyle maneuvers. DNR, USA is currently spending $11.02 per meter for rubber sheet material, 250 mm wide by 2.1 mm thick, supplied from HBK chemical in Austria. Not included in this price is the cost of freight and duty, which adds an additional 20% to the cost.ii It is believed that a cost-effective alternative material can be produced domestically. This alternative would reduce material costs, freight costs and lead-time. The problem is evaluating the material currently being used and finding a suitable replacement.
 The author of this case study succinctly defines the technical and cost constraints of the Snowboard. In the sentence above the reader clearly knows what the key problem is. Below a mathematical model of the Snowboard is given that enables the reader and author to see what the key performance indices are. Thus conciseness is combined with precision to define the technical and cost variables that are used to optimize the materials selection for a Snowboard. Not much fluff or unnecessary verbiage.

The engineering department has come up with a mathematical model of the tip and tail of the snowboard, in order to create a performance indices for the selection of potential materials.

The Mathematical Model

The Assumptionsiii:

1) The boards can be modeled like a composite sandwich beam, with glass fiber reinforced facings.
2) The laminate is symmetric about its midplane.
3) The thickness of the top facing is as thick as the bottom facing, and both facings are half as thick as the core.
4) Because the fiberglass reinforcement is a triaxial weave it is assumed to have the same properties in all directions.

Model:
Figure 1. This diagram illustrates the idea of a sandwich board.

The deflection through the middle of the tip and tail sections of the board can be described as:
 
d = do sin ax sin by Equation 1
where:
do = the maximum deflection of the mode panel
a = p/a
b = p/b
a, b = length of the sides of the model panel

Taking the shear deformation of the core material into account, the maximum deflection becomes:
do = do'(1 +  h) Equation 2
where:
h = a correction factor =  (ctR)/k’ Equation 3
where:
c = core thickness
t = facing thickness
R, k’ = constants that vary for each individual case
k’=Gc(l + (b2/a2)) Equation 4
R = [(Efp2/(2la2))*((b2/a2) + 2A)] Equation 5
where:
A = Ef + 2lGf
Ef= Young’s modulus of the facings
Gf= Shear modulus of the facings
Gc = Shear modulus of the core

Through the relationiv:
E = 2G(l + v)

The facing shear modulus term becomes:
Gf (Ef7(2(l + v)))
Therefore,
R = [(Efp2/(2la2))*((b2/a2) + (a2/b2) + 2v + (l/(l+v)))]  Equation 5a

Setting everything except the Ef term equal to a constant (Q):
(p2/(2la2))*((b2/a2) + (a2/b2) + 2v + (l/(l+v)) = Q (a constant)

The equation for R then becomes:
R=Q*Ef  Equation 5b

The equation for the maximum deflection in the model panel then becomes:
do = do' (1 + [ctQ/(1 + b2/a2 ) )*(Ef/Gc)] Equation 2a

Based on this equation the key performance index is determined to be (Ef/Gc), which
when minimized gives the best qualifying materials. The same result can be reached by
maximizing the ratio (Gc/Ef). Where Gc = shear modulus, and Ef = Young’s modulus.
This concludes the authors analysis of the problem. After this background the author begins the analysis of the optimal material. He used the Cambridge Materials Selector as  screening tool. As discussed in class, other tools are available to help further refine the selection process.

Using the performance index with the Cambridge Material Selector software to select the preliminary materials, weighting factors will be used to narrow the candidate materials.

1. Harper, J., Case Study: A look inside Snowboard Construction Components, 1998, pp 3-4.
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Materials selection for a High Performance Ice Axe1

Background

Ice Climbing

In general, the ice climber is outfitted with crampons fitted tightly over plastic boots and an ice axe in each hand. The ice climber may or may not have a harness with accompanying rope, "Protection" (i.e., ice screws), and "belayer" (climbing partner serving as anchor on the other end of the rope.) Either way, the ice climber ascends by alternately kicking the front points of his crampons and the swinging tips of his ice axes into the ice. The climber ideally always has three points of contact in the ice while repositioning the fourth point into a new, usually higher, position. Figure 1 illustrates an ice climber at work.

Ice climbing can assume a number of different forms depending on a number of different-parameters, including ice steepness, quality, and thickness. Ice can vary in steepness, from a gentle 45 degree slope to 30 degrees or more overhanging. Ice quality can also vary, depending on water quantity of the ice and its corresponding hardness and cohesiveness. Ice can also vary in thickness. Some ice climbs go up waterfalls that are meters thick while some travel tenuously up thin smears of ice that are only a quarter to half an inch thick in places. Ice can also be covered by layers of snow of varying thickness.

Steeper ice requires more upper body strength and a more refined technique. Higher performance tools
are highly beneficial in this environment. In general, the tools being considered for this proposal are most applicable when the angle exceeds 80 degrees. These tools can be used in virtually any ice conditions, but are most advantageous when the ice is of "good" quality. (Good quality means that the ice is solid enough for the ice pick to become rigidly fixed in it, sufficient to bear the weight of the climber.) These tools can be used for both thick and thin ice. Thinner ice requires more delicate precision and once again, better tools help a lot.
The author is wordier in this case study , but this still works because it is well written and because it is reasonable to assume that the readers are less familiar with ice climbing than with Snowboarding.
 

The ice axe
This is a good description of the ice axe and its main components.

The main parts-of the ice axe are the axe head, the shaft, the spike, and the leash.. Figure 2 is a picture of BD’s Black Prophet ice axe. Both the head and the spike are permanently bonded to the shaft. The head has holes-into which can be secured a number of interchangeable stainless steel components, including the adze, the pick, and the hammerhead. Two such tools can be fixed on the axe at any given time. The adze is used for softer/poorer quality ice, chopping steps, and/or wedging in rock cracks, the pick is used for hooking rocks and/or fixing in harder ice, and the hammer is used for hammering pitons and/or torquing in rock cracks2. The hammerhead and axe head together lend swing weight. The spike is helpful in allowing the axe to be sunk handle first in snow for use as an anchor or as a cane. A nylon webbing leash is also attached to the hammer head; this leash acts as a retention device and also allows the climber to hang by his wrists from the axes once they have been fixed in ice instead of having to hang on with his hands (i.e., hang from one’s skeleton rather from one’s musculature.)
 
 


Problem Statement
















Scenario
This paragraph could go back to the introduction or the beginning of the background section.

One of Black Diamond’s product lines is the ice climbing line. Included in this line are 4130 CroMo ice screws, CroMo crampons, plastic climbing boots, and a variety of climbing axes. The ice line is an important product line for Black Diamond. Annual sales of ice axes are in the $250,000 to $500,000 range. New market research shows that ice climbing is a burgeoning sport, with a large percentage of the customers fitting the profile of an upper middle class professional with large amounts of expendable income. These individuals typically purchase higher performance products with less regard for cost than the average consumer. Therefore, forecasts are that ice axe sales should be up for companies with "high performance" ice axes. As an engineer for Black Diamond, I have been asked to research different axe shaft3 materials and come to a final recommendation based on the identified functional requirements and constraints.

Performance Requirements / Material Properties
This is again wordier than the snowboard , but the length is justified by providing useful information to the reader. There are many ways to skin the cat regarding length. The overriding question is whether each sentence you write is adding value to the argument you are presenting. In this case they seem to.

Axe weight. The primary constraint is the axe weight. The overall weight of the axe should be kept to an absolute minimum. On an average 120 foot ice climb, the climber will probably need to make ice axe "placements" every 1 to 3 feet. Between 1 and 4 swings are usually necessary for a novice climber to gain a solid placement with the ice axe pick. Consequently, the climber will perform 40 and 480 axe swings per climb. Multiply this number by 5 climbs done in a day and the number of axe swings grows to 200 to 2400. It is obvious that given these large numbers, even ounces will make difference between success and failure at the end of a long day; fatigue from a heavy axe will reduce the climber’s ability to make precise, solid placements. Poor axe placements which are not sufficiently solid to hold the climber’s weight could easily result in injury or even death!

Ideally, the axe should combine an axe head with good swing weight and momentum for penetrating ice with a very lightweight shaft. Since this case study focuses on shaft weight, weight is an important material property to be minimized.

Axe strength. Another critical constraint is the tensile strength of the axe shaft. There will be a bending stress on the shaft since the pick is set into the ice at a perpendicular distance of 8 to 12 inches from the shaft. While no rotational forces are foreseen, the axe must be rotationally stiff enough to resist bending during the actual climbing (these loads are relatively small).

Minimum strength requirements are specified by the European CEN standards. These safety standards are to be met by any product sold in Europe. Since the United States does not have any similar safety standards, Black Diamond ships their axes to Europe to be tested by this organization. The specific testing procedures and loads are called out in the document Ice Tools: Safety requirements and testing methods. This document discusses the safety aspects of all of the axe components. Appendix 1 presents the testing scenario used for shaft strength.

These tests require the axe to be loaded in two orientations with respect to the shaft cross section. In the first test, a force of 3.5 kN is applied at the midsection of the axe with the axe supported at both ends. This loading generates a maximum moment of 437.5 Newton meters (Nm). In the second test, the axe is loaded at one end by a .9 kN force with the other end supported by constraining the pick. This second loading generates a maximum moment of 450 Nm. These moment calculations are included in Appendix 2. Calculations were then performed to determine the minimum tensile strength required of a shaft of solid cross section (i.e., not hollow) to prevent failure when exposed to these loads. The first test indicated a minimum tensile stress of 407.6 MPa, while the second test indicated a minimum tensile stress of 186.4 Mpa. These calculations are included in Appendix 34. Based on these results, any material which does not have at a minimum tensile strength of 407.6 Mpa must be discarded as a candidate.

Axe balance/feel. The weight distribution and balance of the axe are absolutely critical. Even a light axe which is improperly balanced will not allow the climber the necessary precision and fluidity for accurate placements. Sufficient weight must be provided in the axe head to provide momentum for the pick to penetrate the ice. This "feel/balance" requirement for the axe as a whole requires a highly rigid shaft. Therefore, Young’s modulus is an important property for the axe shaft.

Vibration damping. The handle material should dampen the vibrations associated with swinging the axe head into the ice. This translates into loss coefficient as a material property to be considered in the selection process. (Loss coefficient is a measure of how well a material dissipates energy upon impact. A material with a high loss coefficient will have good damping properties; a material with a low loss coefficient will vibrate upon impact, sending shock waves into the user’s hand and arm.)

Toughness. The material must be tough enough to withstand a significant impact. For instance, the axe could easily be dropped from 100+ feet. Also, the axe shaft is constantly exposed to high impact loads during use from "miss-hits". Miss-hits occur when the axe is swung toward the ice and instead of the pick penetrating the ice, the axe shaft accidentally smashes into rock or ice. While the manufacturer can recommend retirement of the axe under these conditions, in the real world a climber will undoubtedly continue to use a $350 ice axe unless it shows visible structural damage. The designer should attempt to accommodate such inevitabilities if possible by considering materials with high fracture toughness.

Endurance limit. The material should have a relatively high endurance limit because of the large number of impacts that this product will be exposed to. Endurance limit is loosely defined as the largest stress at which a material can withstand an infinite number of loadings without failure. A material with an endurance limit higher than the maximum loads that the shaft will be exposed to in a miss-hit situation will be beneficial.

Geometry. The cross-sectional area is fixed since the axe must be able to be comfortably held by a gloved hand. This case study assumes an elliptical cross-section of the shaft with dimensions of 2/3" by 1.5", which are the approximate dimensions of the shaft of the BD Black Prophet axe. All calculations in this case study are based on this fixed outer elliptical profile. (As discussed below, however, this cross section is not necessarily solid, but only as thick as it needs to be for each material to resist failure in the CEN tests.) A fixed shaft length of .5 m is also assumed.

Price point considerations. The new capital opportunities created by a growing climber population have allowed for the continued development and refinement of climbing hardware which incorporate the latest advances in engineering materials. New innovations in equipment, in turn, allow for new standards to be reached by the climbing elite and novice alike. Climber’s safety as well as performance have benefited from this cycle.

None of these advances have come cheaply, however. Climbing equipment is expensive, with ice climbing equipment being among the most expensive of all. For example, initial costs to the starting ice climber can easily exceed $1000. As with other high-end equipment intensive sports (e.g., windsurfing, skiing, Mt. biking), in general there usually is a market for high performance products. This is especially true in a potentially life-threatening sport such as climbing, where to buy cheaper, lower quality equipment is very risky to the consumer. A more expensive product which works well is likely to sell better than a less expensive product which does not really work! This premium on quality is especially true for a Black Diamond product because BD has developed a valuable reputation as the supplier of premier high performance climbing equipment. To make a "cheap" product which is not durable will hurt its other product lines; this can not be risked.

All things being equal, however, cost should still be minimized! Black Diamond is obviously a
for-profit organization, and as such cost is an important factor. For this study, total cost consists of
material cost and manufacturing cost. (Initial start-up costs for equipment are not considered.)

Marketing factor. Certain materials inherently carry with them an intangible consumer appeal which will help them sell. This "marketing factor" does not necessarily have a direct correlation with performance5. Perhaps this factor can be thought of as being related to "high-tech" by the consumer. Whatever its origins, it seems necessary to give the "marketability" of a material some importance, since selling is an obvious objective.

Material Properties Summary
The summary here lists the variables that will be used in the optimization of the materials selection . The author goes on to use spreadsheets and selection charts to make a good case for his materials choice. This case is available in the library .

The properties to be considered in this case study include:

1. Cann, M., Material Selection for a High Performance Ice Axe, 1998, pp 2 - 5.
2. Rock is referenced since these tools are also used in a mixed climbing environment, where both rock and ice are climbed simultaneously. This is the area of climbing that is exploding in popularity. Tool designs are more toward mixed climbing than pure ice climbing.
3. Previous research has already identified optimal materials for the other axe components; these are not considered as part of this project.
4. These stress calculations are based on a constrained elliptical cross-section of the shall with dimensions of 2/3" by 1.5". All calculations in this case study are based on this fixed outer elliptical profile.
5. As will be seen, Al-SiC metal matrix has a high marketing factor but actually finishes dead last in this case study.
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Last update 9-18-98