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Materials Selection in Engineering
©2003 The Ohio State University
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Overview Factors/Criteria in Material Selection
Function Mechanical Properties Failure Modes Manufacturability Cost Environmental Considerations Decision Making in material selection This presentation will outline the various factors and criteria that play a role in material selection. These factors include Function, Mechanical Properties, Failure Modes, Manufacturability, Cost, and Environmental considerations. Given these Criteria in Material selection, several key points will be presented on methods that can be implemented to make a sound decision when making the final material selection.
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Material Selection and Design
Material Selection is Design-led Properties of a new material can suggest the new product Transistor: High-purity silicon Optical Fiber: High-purity glass The methodology discussed here for selecting materials is design-led: The functional requirements of the design are used as inputs in the selection process Design is an iterative process, and the starting point in many cases is a market need or a new idea. The end point would be a product that fills that need or embodies the idea. It is not always necessary to start from scratch with original design like the mechanical pencil, or zip disk. Development of new materials can offer a unique combination of properties which suggest the new design. For instance, the characteristics of high purity silicon gave way to the transistor, and those of high-purity glass made the optical fiber feasible. Optical Fiber
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Material Selection and Design
Need for a new product can demand the development of a new material Turbine Technology:High-Temperature Alloys,Ceramics Space Technology: Lightweight Composites Conversely, the need for a new product can demand the development of a new material. Turbine technology necessitated the development of high temperature alloys, and ceramics. Space Technology, in which reduction of every pound of material results in a savings of over $10,000, led to the evolution of lightweight composites. Figure: img/pathfinder.jpg The solar-powered Pathfinder in flight. (Pic: Clark University, Worcester, Mass.) University, Worcester, Mass.) The solar-powered Pathfinder in flight Picture: Clark University, Worcester, Massachusetts
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Mechanical Design Deals with function and physical principles
Components must Carry Loads Conduct Heat and Electricity Exposed to Wear and Corrosion Must be Manufactured Limited by Materials Focus of this presentation is the role of material selection in Mechanical Design for Machines and Components Mechanical design, deals with the physical principles, function, and production of mechanical systems. Different from Industrial design in which color, texture and overall customer appeal are key, since that aspect comes after the functionality of the system has been met. Mechanical components must carry loads, conduct heat and electricity, are exposed to wear and corrosion, and they must be manufactured—therefore, it is clear that selection of proper materials is key in the design of such components in order to meet the functional requirements.
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Engineering Materials
Six important classes of materials Metals Polymers Elastomers Ceramics Glasses Composites Successful design exploits and brings out the true potential of materials selected. The goal is to meet a certain profile of properties There are six important classes of materials for mechanical design: metals, polymers, elastomers, ceramics, glasses, and composites which combine the properties of two or more of the others. A successful machine design uses the best materials for the job, and fully exploits their potential. Therefore, in the end it is a set of specific properties that we seek to find—a profile that a material or combination of materials can satisfy.
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Design-Limiting Material Properties
General: Cost Density Mechanical Elastic Moduli Strength Toughness Fracture Toughness Damping Capacity Fatigue Endurance Limit Wear Archard Wear Constant Thermal Thermal Conductivity Thermal Diffusivity Specific Heat Melting Point Glass Temperature Thermal Expansion Coefficient Thermal Shock Resistance Creep Resistance Corrosion/Oxidation Corrosion Rate Parabolic Rate Constant In order to choose a material or series of materials that meet the set of properties that are important to an application, it is necessary to have an understanding of the several design-limiting material properties. These properties are generally discussed in great detail in introductory design classes, and should be quite familiar. Material-specific data can be obtained from any of the various Machine-design texts that are available.
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Menu of Materials Metals Ceramics/Glasses High Moduli
Can undergo Alloying, Heat Treatment Formed by Deformation Ductile Yields before fracture Prey to Fatigue, Corrosion Ceramics/Glasses High Moduli, Hard, Abrasion/Corrosion resistant Cutting Tools Retain Strength at High Temperature Brittle Prey to high contact stresses, low tolerance for cracks The Members of each class share common features, similar properties and processing routes, and even applications. Metals have a relatively high moduli, and can be made strong by alloying as well as mechanical and heat treatment. They remain ductile which allows for them to be formed by deformation, and which also ensures that they yield before fracture. However, partly due to their ductility, metals can fail due to fatigue. IN addition, they are the least resistant to corrosion of all the classes of materials. In comparison, ceramics and glasses have a high moduli, but are also are hard, and abrasion resistant—hence their use in cutting tools. They are also capable of retaining their strength at high temperatures. However, unlike metals, they are brittle, and therefore have a low tolerance for stress concentrations-- like holes and cracks—In addition, they are also weak in tension and cannot handle high contact stress.
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Menu of Materials Composites Polymers and Elastomers
Low Moduli, High Strength High Elastic Deflection Snap fits Corrosion Resistant Easy to Shape Minimize Finishing Operations Temperature Dependent Properties Composites High Moduli, Strength, Lightweight Can be Tough Optimal performance at room temperature Expensive Difficult to Form/Join Polymers and Elastomers are at the other end of the spectrum from Metals, Ceramics and Glass, in that they have a low moduli (roughly 50x less than that of metal), however are very strong. AS a result of this combination, they can undergo large elastic deflection which can make assembly both fast and cheap. When combinations of properties, such as strength per unit weight, are important, polymers are as good as metals. They are easy to shape by molding, and by accurately sizing the mold, and pre-dying the material, no finishing operations are needed. The main drawback is that their material properties are temperature dependent. A polymer that is tough and flexible at room temperature (70 F) may be brittle at 30 F, and yet creep rapidly at 200 F. None have useful strength above 400 F. Composites are favorable in that they combine the attractive properties of the other classes of materials while avoiding their drawbacks. They are lightweight, stiff, strong, and can be tough. Those composites which are centered around a polymer matrix above about 500 F because of softening, however their performance at room temperature can be excellent. Despite their positive traits, composites are expensive and relatively difficult to join or form, so a designer can only use them when the added performance justifies the added cost.
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Materials Selection Charts
Combinations of properties are important in evaluating usefulness of materials. Strength to Weight Ratio: sf/r Stiffness to Weight Ratio: E/r Helpful to plot one property against another Following charts useful in performance-optimization Material Classification is helpful for making an association between a material type and its characteristic properties—again, this is important since material properties limit performance. Almost always it is a combination of properties that factor into whether a particular material can be chosen. For instance, the development of a lightweight design necessitates the use of strength to weight ratio, or stiffness to weight ratio, rather than just the individual values for strength, stiffness, and weight. Therefore in order to get a proper feel for the values design-limiting properties can have, it is helpful to plot one property against another, mapping out the fields in property-space occupied by each material class, and the sub-fields occupied by individual materials. The resulting charts are helpful in many ways since they condense a large amount of information into a compact but accessible form, so they lend themselves to performance-optimizing techniques.
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Speed of Sound in a solid, v
Represented by: As an example, we know that the speed of sound in a solid depends on the modulus, E, and the density, ro. The longitudinal wave speed, v, for instance is V = (E/ro)^1/2, or by taking the logs: log E = log (Ro) +2*log(v) For a fixed value of v, this equation plots as a straight line of slope 1 on the figure shown. This relationship between E and ro allows the use of contours of constant wave velocity on the chart. These contours are the family of parallel diagonal lines that link materials in which longitudinal waves travel with the same speed. It is important to note the format of the chart. The idea here is to represent the relationship between Modulus and density, therefore, E is plotted against the density on log scales. Each class of material occupies a characteristic part of the chart. The log scales allow the longitudinal wave velocity to be plotted as a set of parallel contours. This chart is a simplified version of an actual characteristic Modulus-Density chart In this way, all of the materials properties charts allow additional fundamental relationships of this sort to be displayed. As will be shown on the next slide as well… M.F. Ashby. Materials Selection in Mechanical Design. Pp34 © 1999
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Modulus vs. Density Chart
This chart is an expanded version of the previous one, and is more characteristic of what would actually be used by a designer. Here, it can be clearly seen that the heavy envelopes enclose data for a given class of material. In the ‘Engineering Alloys’ envelope, all of the important different types of alloys can be compared. Under the ‘Woods’ section, the difference between woods that are being used parallel to the grain as opposed to those that are being used perpendicular to the grain can be viewed. As in the previous chart, the diagonal contours show the longitudinal wave velocity. In addition, Guide lines of constant ratios E/ro, E^1/2/ ro, and E^1/3/ ro can be used to allow the selection of materials for minimum weight and deflection-limited design. M.F. Ashby. Materials Selection in Mechanical Design. Pp37 © 1999
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Material Indices A method is necessary for translating design requirements into a prescription for a material Modulus-Density charts Reveal a method of using lines of constant to allow selection of materials for minimum weight and deflection-limited design. Material Index Combination of material properties which characterize performance in a given application. The question to ask now, is how to translate the design requirements for a machine or component into a prescription for a material. This Selection is dependent on the function for which the component is being designed, the constraints it must meet, and the objectives the designer has selected to optimize the performance of the component. From the Modulus-Density charts shown on the previous slides, a clear relationship is established between the various lines of constant modulus to density ratios, and the selection of a material for weight and deflection limited design. The use of the Modulus-Density chart implied that the design in question could be optimized by using a material which had a specific Modulus-Density ratio. IN a particular design, the material index is a combination of material properties which characterizes performance in a given application Therefore, in the case of a design limited weight and deflection, the modulus-density ratio would be considered to be the material index. This should become more clear in subsequent slides.
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Material Indices and Performance
Combination of material properties which characterize performance in a given application Performance of a material: Here we restate the fact that the material index is a combination of material properties which characterize the performance of a component in a given application. The performance of an element can be described as being dependent upon the functional requirements, geometric parameters, and material properties of a a design. These variables are denoted as F,G, and M respectively. These functions are generally separable as shown in the bottom equation, therefore, the separate functions, f1,f2,f3 can be evaluated individually and multiplied together. This method of displaying the parameters of performance implies that an optimum subset of materials can be identified without solving the complete design problem or even knowing all the details of the design
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Simplification of Performance
Performance for all F and G is maximized by maximizing f3 (M) f3 (M): Material Index f1 (F) f2(G) : Related to Structural Index Each combination of function, objective, and constraint leads to a material index. In fact, being able to separate the functions enables an enormous simplification since we can state that the performance for all F, and G is maximized by maximizing function 3, or rather, the material index. The remaining functions of F, and G are related to the structural index, which will not be addressed here, but can be obtained from reference texts on Materials Selection (ASHBY). Each combination of function, objective, and constraint leads to a material index that is characteristic of the combination. The method presented here is general, and can be applied to a wide range of problems. A catalogue of such indices can be obtained from reference texts (ASHBY).
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Example: Calculation of Material Index
Design: cylindrical tie rod Given length, ‘l’ carries tensile force, ‘F’ with minimum mass Objective Function Mass (m) = Area (A) * Length (l) * Density ( ) Goal: minimize ‘m’ by varying ‘A’ Constraint: A must be sufficient to carry tensile load, F (failure strength) A simple example can help demonstrate how material index can calculated and maximized for optimizing performance. The design here calls for a cylindrical tie rod of specified length, l, to carry a tensile force, F, without failure; the tie rod must be of minimum mass. Since we seek to minimize the mass, the objective equation gives the relationship between mass of a rod, and the geometry and material of the rod. Maximizing the performance in this case refers to minimizing the mass while still carrying the load, F, safely. The safety factor is usually included on the right side of the second equation and is divided from failure strength, however, is left out here for simplicity.
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Example: Material Index (Continued )
By eliminating ‘A’ from these equations we obtain The lightest tie which will carry F safely is that made of the material with the smallest value of Therefore, the material index can be defined as A similar calculation for a light, stiff tie leads to the index My eliminating cross sectional area from the equations, we can relate the objective function to that for failure strength to obtain an expression for mass in terms of loading, geometry, and material properties. We can easily see from the first equation on this slide, that the lightest tie that will carry a force safely is that made of a material with the smallest value of density to failure strength ratio. Since we are interested in maximizing the material index, we can define M as the failure strength to weight ratio which can now be used in the following charts to help in selecting the appropriate material. IN the same way, we can calculate the material index in terms of the stiffness to density ratio.
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Strength vs. Density Chart
Therefore, to optimize the design of the tie rod, the Strength-Density chart similar to this can be used. Here we observe that Guide lines of constant failure strength to density ratios can be used to obtain minimum weight, yield-limited design. M.F. Ashby. Materials Selection in Mechanical Design. Pp39 ©1999
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Other Materials Selection Charts
Modulus-Relative Cost Strength-Relative Cost Modulus-Strength Specific Modulus-Specific Strength Fracture Toughness-Modulus Fracture Toughness-Strength Loss Coefficient-Modulus Facture Toughness-Density Conductivity-Diffusivity Expansion-Conductivity Expansion-Modulus Strength-Expansion Strength Temperature Wear Rate-Hardness Environmental Attack Chart In this way, several materials charts are available to compare various combinations of properties. From this list, we can get a clear view of other factors which play an important role in the materials selection process, in addition to material properties. These factors include Material Cost as well as Failure properties such as Wear, and Environmental Corrosion. All of these factors are related to each other in some way, and this will now be the topic of discussion.
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Failure Can be of many types
Wearout Fracture Corrosion Important to be aware of appropriate repair methods available Failure mode can be anticipated based on material type Pipeline Failure Failure in general can be of many types—a material can undergo Wearout, Corrosion, or Fracture. The picture to the right is an example of a section of corroded pipeline. In many cases, a designer can consider the anticipated failure mode, and therefore, has the ability to chose a material that can be repaired easily. Wearouts can be repaired by building up the worn surface. In the case of metal, depositing weld metal, plasma spray, or electroplating may be possible if the surface permits such procedures. Fractures can be repaired by welding if the material is weldable, however, it is difficult to restore the original strength of the component, and the designer must account for the property change that accompanies the fabrication. There are many forms of corrosion, and aside from using materials that are corrosion resistant, onset of corrosion can, at best, be delayed by protective coatings, and preventative measures depending on the environment in which the component is to be used. If a particular corrosive material must be used, then it is necessary for the designer to ensure ease of repair and replacement of the part or component. Earlier in the presentation we discussed the Menu of Materials which briefly indicated the characteristics associated with the 6 material classes. Metals were ductile, but most likely of all the classes to be subject to corrosion. Ceramics and Glasses, on the other hand were corrosion resistant were brittle. Metals, Ceramics and Glasses could all tolerate high temperature whereas Polymers, Elastomers, and epoxy-based ceramics had temperature dependent properties which predisposed them brittle behavior at low temperatures, and creep at high temperatures.
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Environmental Attack Chart
The chart shown is the environmental attach chart which shows a comparative ranking of the resistance of materials to attack by six common environments. All engineering materials are reactive chemicals, so their long-term properties, including strength and stiffness, depend on the rate and nature of their reaction with their environment. The reaction can take on the form of corrosion, oxidation, or any other number of forms. In some cases, a thin, stable, adherent film is developed, while others are more damaging since the effective load-bearing capacity actually decreases without any apparent loss of section. This is merely a brief introduction to a problem which requires detailed and complex expertise, and the information on this chart should be used for the broadest of guidance only. M.F. Ashby. Materials Selection in Mechanical Design. Pp62 © 1999
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Manufacturability The material choice must be compatible with the manufacturing process and configuration Radius to which a sheet metal is bent depends on ductility Residual stress due to cooling of a cast part may result in hot tearing The next factor to be considered here, is that of Manufacturability. When making the decision of how to manufacture a product, it is important to keep in mind the limitations of the selected material in a given manufacturing process. The ‘Menu of Materials’ presented earlier outlines some of the basic characteristics of the 6 classes of materials including limitations due to temperature or nature of application. The material choice must be compatible with the manufacturing process and configuration. For instance, The radius to which a sheet metal may be bent will depend primarily on the ductility of the material. Therefore, the decision about bend radius cannot be made independently of material choice. In addition, if material is particularly susceptible to hot tearing— cracking during or immediately after solidification—and it is cast in a configuration such that stresses arise as the part shrinks when it cools in the mold—the resulting part will be scrap. The figure shown is an example of a water pump that was manufactured by casting. The various properties associated with specific types of materials predisposes them to a particular type of manufacturing process in order to create the component. Pg. 24 G.T. Murray handbook of materials selection for engineering application. Cast water pump
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Factors in Manufacturing Processes
Castability Formability/Workability Machinability Coatability Heat Treatment Therefore, it is important to take into consideration the effect of manufacturing process on the choice of materials before making the final material selection. Some of the factors that play a role in manufacturing processes are displayed here. For instance, as mentioned in the previous slide, mechanical properties of many cast materials are dependent on cooling rate during and after solidification. Therefore, the properties will vary with respect to location within the casting according to wall thickness. IN addition Variability in cooling rate from one casting to another in the same lot, and variability in internal unsoundness increases overall statistical variance of mechanical properties of a cast part. Formability and workability refer to the ability of the material to successfully withstand the plastic deformation that may be required during manufacturing. Therefore, the material must be ductile. Machinability involves the removal of material from a work piece and the creation of a new surface. It refers to the ease with which material can be removed, and this can refer to the life of the material after machining, the amount of power required to remove a given amount of material, and resulting surface finish. For instance, the resulting fracture necessary to separate a chip from the work piece may leave cracks penetrating through the material which can lead to a bad surface finish and decrease the life of the resulting part. Coating a part may be necessary for protective as well as decorative reasons. The material selection decision for the base material must include consideration of the fact that the finished product will have different properties at different locations. Heat Treatment may be used for softening a previously cold-worked or hardened material, or for strengthening those materials whose microstructures are susceptible to hardening by heat treatment. Materials can undergo expansion and contraction as a result which may cause residual stresses. Understanding the processing method for a material is vital to a thorough failure and cost analysis. Before a component can fail, it must first be created or produced, and the method of production will have a direct effect on the cost to the consumer, which will be presented next.
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Cost Effectiveness and Value Analysis
Extent to which the appropriate performance criteria are satisfied Cost What has to be paid in order to achieve that level of value Material selection in a design must provide most value for the least cost The process of selecting a promising list of candidate materials for a given application will be carried out initially in terms of the required properties to meet the function and allow production of the product, but final decisions will always involve considerations of cost, therefore, we shall look at this next. It is important to understand the concept of cost relative to the value of the product. The value is the Extent to which the appropriate performance criteria are satisfied. The cost, on the other hand, is What has to be paid in order to achieve that level of value. The amount of ‘What is paid’ to achieve the level of value has a range of flexibility associated, and the goal in material selection is to achieve the most value for the lowest cost, both to the manufacturer, as well as to the consumer. Selection and Use of Engineering Materials FAA Crane, and JA Charles
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Cost Effective Materials
Selected material must be able to meet the function and allow production of the product at an acceptable price. Savings incurred from the quality of a material may outweigh the initial cost in certain applications. Conversely, an inexpensive, low quality material may meet the needs of a product in other applications. Expert judgment is necessary to ensure that a chosen material will not only provide adequate in service performance, but will be acceptable to the producer, in the sense of combining the right price with the prospect of being fabricated economically. During the material selection process, first cost of a material can sometimes seem to be impossibly high, however some materials may appear incredibly expensive per unit volume, but will perform in a unique way for long periods of time without the need for maintenance. For example, a small, high-temperature bearing buried in an aircraft jet engine may be worth its weight in gold if it significantly reduces the need for dismantling to replace a cheaper, worn-out component. Alternatively, a variety of materials may be acceptable for use in the design of an object like a gear in a disposable camera. IN this case, the material must be chosen early and the goal in this case is to weigh the cost of the material with ease of manufacturability, as well as the target market and their willingness to pay for the product. Obviously, the life span of any disposable object would allow the use of a cheap plastic material that would in turn keep the cost to an acceptable minimum. EH Cornish
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Cost and Material Selection
Many factors influence the cost of a material Composition Compound Stability Relative Abundance Supply and Demand Many factors can influence the cost of a basic raw material. Although these will not be discussed in length here, it is important to recognize the role each of these factors has on cost. The cost of composition of the material refers to the metallurgical complexity and degree of purity required. In the case of a metal, a metallic alloy is made up a basis metal of a certain purity to which is added the required range of alloying elements, either as pure metals or as hardeners. The higher the purity of the basis metal, the more expensive the alloy will be. In addition alloying elements can be considered to be more rare than the basis element, so when costs of Nickel, for example, are high, austenitic stainless steel prices may go up. In metals, the more stable the compound in which the element is found, the greater will be the amount of energy and thus the cost in the process of reducing that compound for the recovery of the metal value. Therefore, the more easily a metal can be extracted without the need for purification, the cheaper it is. Relative abundance, refers to the fact that less concentrated a material source is, the more effort must be devoted to its extraction. Therefore, iron, where the reduction from oxides is only marginally more energy-consuming than copper and which has also the riches and more easily recovered ores, is the cheapest metal. The elementary theory of economics considers that the price of a commodity is fixed by a unique equilibrium between supply and demand. This price is given by the point at which the demand curve represented by, ‘D’, intersects the supply curve, ‘S’. An increase in the supply would be represented by a shift in the supply curve to right, ‘S prime’, which would result in a decrease in the demand, and therefore, price. FAA CRANE and CHARLES Picture: image002.jpg
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Recycling Recycling of packaging material and certain consumer products is rapidly becoming required by law Material Selection decisions must include consideration of ease of recovery and recycling Current Impediments Components made of mixed plastics Use of plating and coating on base material The recycling of plastic packaging material and certain consumer products notably automobiles and electronic goods, is rapidly becoming required by law in many jurisdictions. IN the design of such products, material selection decisions must include consideration of the ease of recovery and recycling. Recovery includes the ease of disassembly so that the different materials may be separated appropriately. Assembly and disassembly methods may include the use of snap-fit components and the material must be strong enough to withstand the assembly stresses and the stresses encountered in operation—but not so strong that disassembly procedure is unnecessarily difficult. Recycling directly into new products that have essentially the same characteristics as the former ones is one way of reusing the material. however, because of degradation that takes place during recycling, these products are usually designed to have less demanding applications. One impediment to the successful use of recycled material is the insistence by designers on the use of more than one type of plastic in a product. Separation is possible, but expensive, so it is preferable to minimize the use of mixed materials. Therefore an important aspect of the material selection decision may be to reduce the number of different types of materials in the product, specifically to enhance the recyclables of the product. Any plating or coating on the base material also complicates the recycling process, therefore, designs using materials that do not need the foreign material should be considered. Plastics are often favored in such applications because they can be colored instead of painted or plated for appropriate appearance.
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What Next? Many factors involved in material selection process
Each must be taken into account before selection can be made Next Step Selection! There are many factors involved in the material selection process, and some of the key ones have been presented here. Each of these factors and criteria are critical in the overall decision-making process. Now that these factors have been identified, the next step is to actually complete the selection process
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Selection Process Selection among alternatives can be difficult given Factors and Criteria that must be taken into account Experience and judgment can be sufficient at times Formal decision making process can be helpful when there is no one obvious choice of material Selection from among alternatives requires decisions, and sometimes experience and judgment are sufficient to permit a sound decision without a formal process. This is especially true when a candidate material has some outstanding characteristic, or all but one have some serious deficiency. When there is no obvious choice, confidence in the decision can be enhanced by using a formal process.
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Decision Making in Materials Selection
Quantify importance of each desired characteristic Weighting Factor Quantify ability of a candidate material to satisfy these requirements Rating Factor Material Indices Combine Weighting and Rating factors to determine material that offers the best compromise justice Many methods have been developed to formalize the decision process. Mainly, these methods attempt to create an objective way to First Quantify how important each desired characteristic is by determining a weighting factor Second Quantify how well a candidate material satisfies each requirement by determining a rating factor—the material indices presented earlier are considered to be a type of rating factor that can be used to objectively consider all possible materials on a particular material selection chart. And Third The Weighting and Rating factors can be combined to determine which material offers the best compromise There are several mathematical ways all of this can be done including through the use of matrices and computer programs. MURRAY
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Final Material Selection
Selection of Material Implementation of Weighting and Rating factors to optimize the various factors and criteria including Function Manufacturability Cost Further information can be obtained from the many reference texts available on material selection The final material selection decision will, therefore, take into account the various factors and criteria that play a role in the overall production of the product through the use of sound decision making procedures. The methods outlined herein are an introduction to the material selection process for machine and component design, and viewers of this presentation are encouraged to refer to the many texts and resources available on this topic for further elaboration.
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Credits This module is intended as a supplement to design classes in mechanical engineering. It was developed at The Ohio State University under the NSF sponsored Gateway Coalition (grant EEC ). Contributing members include: Gary Kinzel…………………………………. Project supervisor Amita Danak..……………. ………………... Primary author Amita Danak………………... ……….…….. Module revision M.F. Ashby, Materials Selection in Mechanical Design. Butterworth-Heinemann. Boston, MA. © 1999 G.T. Murray, Handbook of Materials Selection for Engineering Applications. Marcel Deckker, Inc. New York, NY. ©1997 E.H. Cornish, Materials and the Designer. Cambridge University Press .New York, NY. © 1987 F.A.A. Crane, J.A. Charles, Selection and use of Engineering Materials. Butterworths. Boston, MA. © 1984
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Disclaimer This information is provided “as is” for general educational purposes; it can change over time and should be interpreted with regards to this particular circumstance. While much effort is made to provide complete information, Ohio State University and Gateway do not guarantee the accuracy and reliability of any information contained or displayed in the presentation. We disclaim any warranty, expressed or implied, including the warranties of fitness for a particular purpose. We do not assume any legal liability or responsibility for the accuracy, completeness, reliability, timeliness or usefulness of any information, or processes disclosed. Nor will Ohio State University or Gateway be held liable for any improper or incorrect use of the information described and/or contain herein and assumes no responsibility for anyone’s use of the information. Reference to any specific commercial product, process, or service by trade name, trademark, manufacture, or otherwise does not necessarily constitute or imply its endorsement.
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