Materials Selection in Engineering ©2003 The Ohio State University

Overview Factors/Criteria in Material Selection Function Geometry 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.

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.

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.

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.

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.

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.

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.

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

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

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.

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

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).

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.

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.

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

Strength vs. Modulus Chart

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.

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.