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MATERIALS SELECTION AND FAILURE ANALYSIS

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Mechanical Properties of Materials

The minimum force (load ) at which a permanent dimensional changes will result in the material used,

The maximum force (load) the material can withstand without breaking,

How flexible or rigid the selected material is? How resistant the material is against impacts or sudden /rapid loading?

How easily the material can be stretched, bent or generally shaped by applying external forces (loads)?

How hard the material is?

How strong the material would be , if the nature of loading or working temperature is varied?

Fig. 1

1

Elastic DeformationThe dimensional or shape changes in a material disappear if the applied external force is removed.

Deformation of Materials

Plastic DeformationIn this case the applied external force brings about a permanent dimensional change in the material and the material will not regain its initial dimensions even if the force is removed.

F F

F F

original

Fig. 2

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1

F

F

Elastic Deformation (Atomic Scale)

F

F

Fig 3

4

F

F

F

F

F

F

Plastic Deformation (Atomic Scale)

Fig 4

5

diameter or thickness

width

CYLINDRICALCross Section

RECTANGULARCross Section

test piece

grip / jaw

gauge length(L0)

FF

Tensile Test

Fig 5

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6

A

B

C

DF

Extension (mm)

L

o

a

d(N)

Proportional Limit ,(point B)The Force beyond which the Force - Extension variation is no longer linear.

Off set Yield Force or Point 0.2% Proof Force, (point C)The Force (FY) beyond which the material is deformed plastically.

Tensile Force (FST) or Ultimate Tensile Force (UTF), (point D)The maximum Force the material can tolerate without failure.

Fracture Force, (point F)The Force at which the material breaks (fails).

M

Load-Extension graph

UTF

Fig. 6

7

A

B

C

DF

Strain

S

T

R

E

S

S(MPa)

Proportional Limit ,(point B)The stress beyond which the Stress-Strain variation is no longer linear.

Off set Yield Strength or Point 0.2% Proof strength, (point C)The Stress (Y) beyond which the material is deformed plastically.Tensile Strength (ST) or Ultimate Tensile Strength (UTS), (point D)The maximum Stress the material can tolerate without failure.

Fracture Strength, (point F)The Stress at which the material breaks (fails).

M

AF A= Initial Cross sectional AreaF= Applied Force (Load)

= Stress ooof

LL

LLL

TS

Fig. 7

8

The AB line is also referred to as the Hooks line and its slope is known as the modulus of elasticity (E) according to Hooks law;

E

oo

ofL

LL

LL

= StrainLo = Initial gauge length

Lf = Final gauge length

AF

A= Initial Cross sectional Area

F= Applied Force (Load)

= Stress

The unit used to express stress is called Pascal (Pa) which is a force of 1 N applied over an area of 1 m2 (Pa = N/m2). 1 MPa= 106 Pa, 1 GPa=109Pa, 1GPa=103 MPa

Fig. 8

Eq. 1 Eq. 2

Eq. 3

o

o

o

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9

Material Yield Strength(MPa) Youngs Modulus(GPa)

Aluminum Alloys 35-600 60-80Copper Alloys 70-1000 100-110

Steels 200-1700 110-115Tungsten Alloys 900-1800 300-450

Nylon 40-120 2-3.5PVC 30-40 1.5-2.5

Epoxies 25-80 1-6Alumina 2000-5000* 200-350

SiC 5000-9000* 400-500Diamond >9000* 900-1000

* compressive strength (data extracted from the book by M.F.Ashby, materials selection in mechanical design,pergamon press,1992.)

Table 1: Yield strength and modulus of elasticity for several materials.

Fig. 9

(Figs. 1-9: R. Ghomashchi, 1999)

Kalpakjian, 2nd edition1991 (both Tables)

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Engineering Strain (e) = ,

Eq. 5 Remember: reduction in area should not be considered as equal to engineering strain.

True Strain

=ln

Eq. 6

Engineering stress vs. True stress If the applied load is divided by the instant cross sectional area of the test piece, the stress is called true stress and has the following relationship with strain

(Eq. 4) n = strain hardening exponent K= Strength coefficient

(CallisterBook)

Fig. 11: Comparison between true stress and engineering stress

Fig. 10: Stress-Strain graph for Brass and Materials with and without a distinct yield point (Callister Book)

Ductility: Amount of plastic deformation at fracture (% elongation or % area reduction). The value of Elongation% and Area Reduction% are different.

Toughness: Ability of a material to absorb energy before failure Energy required to propagate a crack to cause failure, (Area under the True stress-Strain Curve, = ) (Eq. 7)

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Fig. 12: True stress-true strain for several engineering alloys

The beginning of necking corresponds to the highest stress the material can take, Tensile strength (TS or UTS). At necking, = n, so metals with larger (n) can deform uniformly and with greater amount. (See Tutorial for an example)

4

Kalpakjian book, both Fig & Table

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Effect of Strain rate ( : it is an expression for speed of deformation a) Engineering strain rate

.

(Eq. 8)

V is the speed of deformation, (Ram speed)

b) True strain rate ()

.

(Eq.9)

True strain rate decreases with specimen stretched in tensile test.

Fig.13: Engineering stress-strain behaviour for iron at three temperatures (Callister book)

Fig 14: The effect of temperature on the modulus of elasticity for various materials. (Kalpakjian book)

Effect of Temperature on Engineering Stress-Strain curve;

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Effect of strain rate on Materials strength As increases, so tensile strength

(Eq. 10) C = strength coeff. m = strain rate sensitivity exponent

Fig. 15: The effect of strain rate on the ultimate tensile strength of aluminium. Note that as temperature increases, the slope increases. Thus tensile strength becomes more sensitive to strain rate as temperature increases. Source: After J. H. Hollomon.

10

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Compression

Forging, rolling, extrusion compression loading (ho and h are initial and instantaneous height of work piece)

(Eq. 11)

(Eq. 12) In plane strain compression test (used to simulate rolling) the width remains constant and the yield strength in plane strain (`y) is;

1.15 (Eq. 13) (Fig. - Kalpakjian book)

Tables and graph - Kalpakjian book

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Torsion: To study forgeability, the greater the No. of twist prior to failure, the better (greater) forgeability

Shear modulus/ modulus of rigidity (G); shear stress (), shear strain (), Poissons ratio ()

(Eq. 14) For most metals, E is about 2.6 times G.

t = thickness of the reduced section The length of the reduced section (Fig - Kalpakjian book) = Angle of twist (radian) T= torque Note that unlike tension and compression tests, we do not have to be concerned with changes in the cross-sectional area of the specimen in torsion testing. The shear stress-shear strain curves in torsion increase monotonically, hence they are analogous to true stress-true strain curves.

(Eq. 15) (Eq. 16)

Tension and torsion true stress-true strain curves for low carbon steel, Dieters book.

Twisting moment (in-lb) is plotted against angle of twist (Dieters book)

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Bending: The measured strength is called modulus of rupture, transverse rupture strength or bend strength. The specimen fails due to tensile forces at its lower surface as the load-specimen geometry is schematically shown below.

The modulus of rupture, (mr), is calculated as;

(Eq. 17) = distance of the specimen surface to its neutral axis M and I = bending and inertia moments of the cross-section respectively. The value of () is half of the thickness for symmetrical specimens such as rectangular or cylindrical geometry. The equation may be employed for both three and four point bend tests. (M) and (I) vary for either test. For three point bend test; (W= width and t = thickness of sample)

1- Rectangular test piece

2- Cylindrical test piece

(R. Ghomashchi, 1999)

Eq. 18

Eq. 19

Eq. 20 - For rectangular samples

Eq. 21 - For cylindrical samples

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Hardness: An important mechanical properties of materials Resistance of a material to indentation of a harder material against its surface

Tensile Strength (MPa) = K (BHN) for steels K=3.45-3.50

(R. Ghomashchi, 1999)

(Eq. 22)

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(R. Ghomashchi, 1999)

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Impact test To study the toughness (KJ/m2) of materials and determine the nature of failure (ductile or brittle) at the working temperature. Also to measure the Ductile-To-Brittle Transition Temperature DBTT.

1- Charpy (metric standard)

PointofImpact

PointofImpact

Charpy test machine Izod test Machine

www.twi.co.uk/content/jk71.html

indonetwork.co.id/instron/412667/instron-impa...

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(Callister Book)

The following references were used in this section.

1- Kalpakjian book, S. Kalpakjian, Manufacturing Processes for Engineering Materials, 2nd edition, Addison-Wesley, 1991

2- Callister Book, W.D. Callister, Jr, Materials Science and Engineering-An Introduction, 3rd edition,, Wiley and Sons, 1994

3- www.twi.co.uk/content/jk71.html 4- indonetwork.co.id/instron/412667/instron-impa... 5- Dieter Book, G.E. Dieter, Mechanical metallurgy, 2nd edition, 1976. 6- R. Ghomashchi Book, 1999, M.R. Ghomashchi, An introduction to Engineering

Materials, University of South Australia, 1999.

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