module_2_lecture_2_final.pdf

8/10/2019 Module_2_Lecture_2_final.pdf

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Module

2

Selection of Materials andShapes


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Lecture

2Selection of Materials - I


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Instructional objectives

By the end of this lecture, the student will learn

(a)what is a material index and how does it help in selection of material for a given

application, and

(b)how to develop material indices considering the appropriate material properties for an

intended service.

Selection of Materials

Appropriate selection of material is significant for the safe and reliable functioning of a part or

component. Engineering materials can be broadly classified as metals such as iron, copper,

aluminum, and their alloys etc., and non-metals such as ceramics (e.g. alumina and silica

carbide), polymers (e.g. polyvinyle chloride or PVC), natural materials (e.g. wood, cotton, flax,

etc.), composites (e.g. carbon fibre reinforced polymer or CFRP, glass fibre reinforced polymer

or GFRP, etc.) and foams. Each of these materials is characterized by a unique set of physical,

mechanical and chemical properties, which can be treated as attributes of a specific material. The

selection of material is primarily dictated by the specific set of attributes that are required for an

intended service. In particular, the selection of a specific engineering material for a part or

component is guided by the function it should perform and the constraints imposed by theproperties the material.

The problem of selection of an engineering material for a component usually begins with setting

up the target Function, Objective, Constraints, andFree Variables. The Function refers to the

task that the component is primarily expected to perform in service for example, support load,

sustain pressure, transmit heat, etc. The Objective refers to the target such as making the

component functionally superior but cheap and light. In other words, the Objective refers to

what needs to be minimized or maximized. The Constraints in the process of material selection

are primarily geometrical or functional in nature. For example, the length or cross-sectional area

of a component may be fixed. Similarly, the service conditions may demand a specific

component to operate at or beyond a critical temperature that will prohibit use of materials with

low melting temperature. The Free Variables refer to the available candidate materials.


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Material Index (M)

The Material Index (M) refers to an attribute (or a combination of attributes) that

characterizes the performance of a material for a given application. The material index allows

ranking of a set of engineering materials in order of performance for a given application.

Development of a Material Index (M) for an intended service includes the following steps.

Initial Screening of Engineering Materials.

Identification of Functions, Constrains, Objectives and Free Variables.

Development of a Performance Equation.

Use constraints to eliminate the free variable(s) from the performance equation and

develop the material index.

Rank a suitable set of materials based on the material index.

Example 1: Selection of Material for a Light and Strong Tie-Rod [Fig.2.2.1]

Figure 2.2.1 Schematic presentation of a Tie-Rod with an axial tensile load, F

Function: Tie-rod to withstand an axial tensile load of F

Objective: Minimise mass (m) where =ALm , where is the material density.

Constraints: (i)Length L is specified, (ii) Must not yield under axial tensile load, F

Free variable: (i) Cross-sectional area, A, (ii) Material

Performance Equation: yA

F , where y is the yield strength of any material,

The Performance Equationcan be rewritten by substituting the cross-sectional area, A, as

yy

)L)(F(mFL

m (1)

So to minimize mass, we have to minimize the term, y . Or other way, we can maximize the

term y for the sake of our convenience (as the available material property charts are y vs.


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format). So the material index, M1 y, in this case becomes and a material with higher

value of M1 is expected to perform better in comparison to a material with lower value of M 1. It

should be noted that theMaterial Indexin this case provides a ratio between the ultimate tensile

strength and the density of the material. Thus, theMaterial Index (M

1

)would provide a premise

to examine if a material with higher weight (density) has to be selected to ensure that the same

has sufficient strength to avoid failure.

Example 2: Selection of Material for a Light and Stiff Beam [Fig. 2.2.2]

Figure 2.2.2 Schematic presentation of a beam with a bending load, F

Function: Beam to withstand a bending load of F

Objective: Minimise mass (m) where = Lbm 2 , where is the material density.

Constraints: (i)Length L is specified, (ii) Must not bend under bending load, F

Free variable: (i) Edge length, b, (ii) Material

Performance Equation:

The Performance Equation can be developed considering the fact that the beam must be stiff

enough to allow a maximum critical deflection, , under the bending load, F. Thus, the

Performance Equation can be given as

31 L

EI)C(

F (2)

where is the maximum permissible deflection, E is the youngs modulus, I is the second

moment of area. The stiffness, S, of the beam, can be written as, = FS and the second moment

of area, I, can be written as, 12bI 4= .

The Performance Equation can now be rewritten by substituting one of the free

variables (edge length, b) as


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5.0

3

5.0

1 E)L(

LC

S12m (3)

The material index, M2 ( )5.0E, in this case becomes and a material with higher value of M2 is

expected to perform better in comparison to a material with lower value of M 2. In other words,

theMaterial Index (M2

) will depict if a material with higher weight (density) has to be selected

to ensure that the same has sufficient stiffness (i.e. E) to avoid bending during service.

Example 3: Selection of Material for a Light and Strong Beam [Fig. 2.2.3]

Figure 2.2.3 Schematic presentation of a beam with a bending load, F

Function: Beam to withstand a bending load of F

Objective: Minimise mass (m) where = Lbm 2 , where is the material density.

Constraints: (i)Length L is specified, (ii) Must not fail under bending load, F

Free variable: (i) Edge length, b, (ii) MaterialPerformance Equation:

The Performance Equation can be developed considering the fact that the beam must be strong

enough so that it does not fail due to an applied bending moment, M, due to the load, F. Thus,

the Performance Equation can be given as

L2/b

I)C(

L

M y2 (4)

where y12bI 4=

is the yield strength of the material and I is the second moment of area. The secondmoment of area, I, can be written as, .

The Performance Equation can now be rewritten by substituting one of the free

variables (edge length, b) as


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)L(LC

F6mor)L(

LC

M6m

3/2y

33

2

22

3/2y

33

2

2

(5)

The material index, M3 ( ) 3/2y, in this case becomes and a material with higher value of M3 is

expected to perform better in comparison to a material with lower value of M 3. In other words,

theMaterial Index (M3)allows the examination if a material with higher weight (density) has to

be selected to ensure that the same has sufficient strength (i.e. f

) to avoid failure during service.

Example 4: Selection of Material for a Light and Stiff Panel [Fig. 2.2.4]

Figure 2.2.4 Schematic presentation of a panel with a bending load, F

Function: Panel to withstand a bending load of F

Objective: Minimise mass (m) where = Ltwm , where is the material density.

Constraints: (i)Length L is specified, (ii) Must not bend under bending load, F

Free variable: (i) Panel Thickness, t, (ii) Material

Performance Equation:

The Performance Equation can be developed considering the fact that the stiffness of the panel

is sufficient to allow a maximum critical deflection, , under the bending load, F. Thus, the

Performance Equation can be given as

33

L

EI)C(

F (6)

where is the maximum permissible deflection, E is the youngs modulus, I is the second

moment of area. The stiffness, S, of the beam, can be written as, = FS and the second moment

of area, I, can be written as, 12wtI 3= . The Performance Equationcan now be rewritten by

substituting one of the free variables (panel thickness, t) as


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3/1

2

3/1

3

2

E)L(

LC

Sw12m (7)

The material index, M4 ( )3/1E, in this case becomes and a material with higher value of M4 is

expected to perform better in comparison to a material with lower value of M 4

The above four examples depict the simple procedure to develop Material Indices for the

selection of suitable material for various structural requirements. These Material Indices can be

used subsequently to shortlist a range of suitable materials from appropriate Material Property

Charts in a graphical manner. TheMaterial Property Chartsdisplay the combination of material

properties like Youngs modulus and density, strength and density, Youngs modulus and

strength, thermal conductivity and electrical resistivity, strength and cost, and so on. Figure 2.2.5

shows a typical Material Property Chart that displays Youngs modulus (in GPa) vis--vis

density (in Mg/m

.

3

) for a range of engineering materials in a log-log scale.

Figure 2.2.5 Material Property Chart of Youngs Modulus vis--vis Density [2]


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Exercise

Choose the correct answer.

1. TheMaterial Index that can be used to select a suitable material for a light, stiff panel is

(a) ( )3/1E (b) ( )E3/1 (c) ( )E (d) ( )3E2. TheMaterial Index that can be used to select a suitable material for a light, stiff tie-rod is

(a) ( )E (b) ( )E2 (c) ( )E (d) ( ) f

3. TheMaterial Index that can be used to select a suitable material for a light, stiff beam is

(a) ( )2/1E (b) ( )E2/1 (c) ( )E (d) ( )2E

4. TheMaterial Index that can be used to select a suitable material for a light, strong beam is

(a) ( ) 3/2f (b) ( )f3/2 (c) ( ) f (d) ( )3E

5. TheMaterial Index that can be used to select a suitable material for a light, cheap and strong

beam is

(a) ( ) m3/2f C (b) ( )fm3/2 C (c) ( ) mfC (d) ( )f3/23/2mC

Answers:

1. (a) 2. (a) 3. (a) 4. (a) 5. (a)

References

1. G Dieter, Engineering Design - a materials and processing approach, McGraw Hill, NY,

2000.

2. M F Ashby, Material Selection in Mechanical Design, Butterworth-Heinemann, 1999.

module_2_lecture_2_final.pdf

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