Mechanical Materials Selection

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Mechanical Design I (MCE 321) L. Romdhane, Summer 2016, 11:16 AM -- 1--

Summer 2016

Materials

Mechanical Design 1(MCE 321)

Dr. Lotfi

Romdhane

[email protected]


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Chapter 2 Materials


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2 Materials

ChapterOutline

2-1 Material Strength and Stiffness

2-2 The Statistical Significance of Material Properties

2-3 Strength and Cold Work

2-4 Hardness2-5 Impact Properties

2-6 Temperature Effects

2-7 Numbering Systems

2-8 Sand Casting

2-9 Shell Molding

2-10 Investment Casting 2-11 Powder-Metallurgy Process

2-12 Hot-Working Processes

2-13 Cold-Working Processes

2-14 The Heat Treatment of Steel

2-15 Alloy Steels

2-16 Corrosion-Resistant Steels

2-17 Casting Materials

2-18 Nonferrous Metals

2-19 Plastics

2-20 Composite Materials

2-21 Materials Selection


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Engineering Materials

The menu of engineering materials. The basic families of metals, ceramics, glasses,polymers, and elastomers can be combined in various geometries to create hybrids


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Tests and Mechanical Properties

Schematically structured data for design allowable and the characteristics of a materialthat relate to its ability to be formed, joined, and finished; records of experience with its

use; and design guidelines for its use


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Tests and Mechanical PropertiesBasic Design-Limiting Material Mechanical Properties and Their Usual SI Units*

HB


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Standard Tensile Test Figure illustrates a typical tension-test specimen and its

characteristic dimensions. The original diameter and the gaugelength , used to measure the deflections, are recorded before thetest is begun

The specimen is then mounted in the test machine and slowlyloaded in tension while the load P and deflection are observed.

The deflection, or extension of the gage length, is given by l-l 0 where l is the gauge length corresponding to the load P. The normal strainis calculated from

0d 0l

In the linear range, the uniaxial stress-strain relation is given byooks law as


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Engineering Stress-Strain Curve (steel) Point el is called the elastic limit is the yield point Point a is usually 0.2 percent of the original

gauge length.

or is the ultimate, or tensile, strength.

y S

uS ut S


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Engineering Materials


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Torsional Strength Torsional strengths are found by twisting solid circular bars and

recording the torque and the twist angle. The maximum shear stress is related to the angle of twist by

where is in radius, is the radius of the specimen, is thegauge length, and is the material stiffness property called theshear modulus or the modulus of rigidity .

max

The maximum shear stress also related to the applied torque as

where is the polar second moment of area of the crosssection.

41

2 J r


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Engineers, when ordering property tests, should couch the instructionsso the data generated are enough for them to observe the statisticalparameters and to identify the distributional characteristic.

Statistical Significance of Material Properties

The stress-strain diagram depicts theresult of a single tension test. If therewere 1000 nominally identicalspecimens, the values of strengthobtained would be distributed betweensome minimum and maximum values.

21 1 438.3

( ) exp2 17.917.9 2

x

f x

has the mean stress 438.3 MPa and the standard deviation 17.9 MPa,denoted as = 438,17.9.

The bar chart depicts the histogram of the probability density. If the data is inthe form of a Gaussian or normal distribution , the probability density functiondetermined by


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Hardness

The resistance of a material to penetration by a pointed tool iscalled hardness . Two most common used hardness measuring systems :

Rockwell hardness , the indenters are described as a diamond, a 1.6-mm-diameter ball, and a diamond for scales A, B, and C, respectively, where the loadapplied is either 60, 100, or 150 kg.

Brinell hardness , the indenting tool through which force is applied is a ball andthe hardness number H B is found as a number equal to the applied load dividedby the spherical surface area of the indentation .

For steels, the relationship between the minimum ultimate strengthand the Brinell hardness number for is found to be

= 0.5 3.4 For cast iron = 0.23 12.5 1.5886

200 450B

H


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Temperature Effect

Strength and ductility, or brittleness,are properties affected by thetemperature for the operatingenvironment.

The effect of temperature on thestatic properties of steels is typified bythe strength versus temperate chart.

There is a substantial increase inductility, as might be expected, athigher temperatures.


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Material Selection Process

The universe of materials and their attributes


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Material Selection

Function, constraints, objectives, and free variables define the boundaryconditions for selecting a material and in the case of load-bearing

components a shape for its cross section.


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Material Selection Process

Choosing a material. Design requirements are firstexpressed as constraints and objectives. The constraintsare used for screening The strategy for materials selection. Th

four main steps translation, screeningranking, and documentation


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Material Selection Chart : Youngs Modulus


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Selection Chart : Youngs Modulus -Density


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Example related to material selection

M properties

material,

G parameters

geometric,

Ftsrequiremen

functionalP

4643 24

3

A D I with

l EI F

k

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E kl

A

P=f(F, G, M) and P= f 1(F). f 2(G). f 3(M)

=

The example is related to how to select an appropriate materiel to design a light, stiff, end-loadedcantilever beam having a circular cross section. is the mass of the beam, the stiffness is related to itsmaterial and geometry and = / . Note that = = (3)/(3 ), where is the end load, deflection, Youngs modulus, the second moment of area

Performance metric P of a structural element is deduced as:

or

and are the diameter and area of the cross section, respectively , we can obtainThe mass of the beam is given by:

2/12/52/1)(

32

E l k m


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Example related to material selection

2/13 )( E M f

To minimize m, we need to maximize 3( ) or maximize

2/1 E M

We have 3( ) given by:

is called material index, and . So, we return now to the draw lines of various

values of this ratio in the bubble chart.21


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Selection Chart : Youngs Modulus -Density


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Material Selection

The specification of function, objective, and constraint leads to a materials index.The combination in the highlighted boxes leads to the index / .


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Material Selection Chart : Strength-density

Courseframework


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Performance Maximizing criteria


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Performance Maximizing criteria

A selection based on the index M = E 1/3 / together with the property limit E > 50 GPa.The materials contained in the search region become the candidates for the next stageof the selection process.


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Material Selection Chart : Strength-density

Specific strengthTo minimize weight


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Material Selection Chart : Strength-Cost


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Example: Material selection

A furniture designer conceives of a lightweight table (see figure): a flat sheet oftoughened glass supported on slender, unbraced cylindrical legs. The legs must besolid (to make them thin) and as light as possible. They must support the table topand whatever is placed upon it without buckling. What materials could onerecommend?

Two objectives should be considered:1) Weight is to be minimized2) Slenderness should be maximized

having a ratio of:Max. resistance to buckling/Min weight


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We wish to minimize the mass of the leg, given by the objective function

= 2

material density and modulus its legs length. The radius of a leg is a free

variable.

The leg is a slender column of and the maximum load, , it must carry aredetermined by the design without buckling.

The elastic buckling load of a column of length and radius is

with = 4/4where is the second moment of the area of the column. Theload must not exceed . Solving for the free variable, , and substituting itinto the equation for gives


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The material properties are grouped together in the last pair of brackets. The weight isminimized by selecting the subset of materials with the greatest value of the material

index

Now slendernessInverting Equation (2) with F crit set equal to F gives an equation for the thinnest leg thatwill not buckle:

The thinnest leg is that made of the material with the largest value of the material index

2 = The selection

We seek the subset of materials that have high values ofE

and . We need the chart again.


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Case study: legs of a Table


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Material selection

Maximize for slenderness

Maximize/

to avoid buckling

Possible choices: Wood Ceramics GFRP (glass fibers) CFRP (carbon fibers)What about hollow tubes!


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Mechanical Design I (MCE 321) L Romdhane Summer 2016 11:16 AM 35

Stiffness and strength vs cost

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Mechanical Materials Selection