ةىودـللاو ةىورـلما تايـساسأ باتـك€¦ · Author Osama Mohammed Elmardi Suleiman Assistant Professor, Faculty of Engineering, Nile Valley University

دوىةـروىة واللـيات املـتاب أساسـك

Fundamentals of Elasticity and Plasticity

يفــتأل

أسامة حممد املرضي سليمان

استاذ مساعد ، كلية اهلندسة ، جامعة وادي النيل

Author

Osama Mohammed Elmardi Suleiman

Assistant Professor, Faculty of Engineering, Nile Valley

University

و 0222 الطبعة األوىل يياير

و 0204 الطبعة الثاىية امليقحة أكتوبر

دوىةـروىة واللـيات املـتاب أساسـك

Fundamentals of Elasticity and Plasticity

يفــتأل

سليمانأسامة حممد املرضي

استاذ مساعد ، كلية اهلندسة ، جامعة وادي النيل

Author

Osama Mohammed Elmardi Suleiman

Assistant Professor, Faculty of Engineering, Nile Valley

University

و 0222 الطبعة األوىل يياير

و 0204 أكتوبرالطبعة الثاىية امليقحة

i

بسم اهلل الرمحن الرحيم

شكر وعرفان

ii

iii

ذمحـمم

i.e.

iv

واهلل املوفق

انمؤنف

خال أضامح محمذ انمرض ضهمان

Osama Mohammed Elmardi Suleiman Khayal

و 6102 أكتىتر

v

تىاخـانمح

i

iii

v

1.11

1.11

1.11

1.11

1.1.16

1.1.19

1.1.111

1.111

1.1.111

1.1.111

1.1.111

1.1.116

1.111

1.116

1.112

1.119

1.111

1.111

1.111

vi

1.111

1.116

1.613

1.312

1.212

1.111

1.111

1.111

1.111

1.111

1.611

1.311

1.211

1.911

1.1161

1.169

1.131

1.121

6.121

6.126

6.126

91

91

كــتاب أساســيات املــروىة واللــدوىة تأليف: أسامة حمند املرضي سلينا خيال

Properties of Engineering Materials

0.0Introduction

( 1/ complexity of extraction 2/ higher cost of technology used )

unmanned drones

0.0Importance of Metals in Industry

i.e.corner stone

ferrous and non- ferrous metals


0.1

Physical and Mechanical Properties of Metals)

Physical Properties

0 Density{

}

0 (Thermal and Electrical Conductivity)

1 Specific Heat Capacity

Q

2 Light Reflection


3 X-Ray Penetration

4 Magnetizability

5 Fluidity

6 Local Fusibility

Mechanical Properties

0 Ductility

tension

compressionbendingtorsiondrawing

wire and tube drawing


0 Malleability

compression

i.e.(forging)

rolling

1 Toughness or Strength

2 Divisibility

3 Hardness

(Hardness: is the ability of a material to withstand scratching or identation)

1.1i.e.

0.2(Engineering Materials Testing)

tensioncompression

torsionimpacthardness


او تشغم انمعادن إنى انشكم انمطهىب(طرق انتصنع ) تشكم (Metal forming and machining)

(Internal conversionتحىم داخه )

انخىاص انفسائح وانكمائح

External conversion)تحىم خارج )

وضائم انتشكم انمكانك

اضتخالص انمعادن

Metal extraction

تنمح انثترول

Petroleum refining

انمعانجح انحرارح

Heat treatment

انمىعح

Fluidity

انماتهح نالنصهار

Fusibility

انهذونح

Plasticity

انماتهح نالنشطار

Divisibility

ضىنح وانطاب انمعذن

انمنصهر

عمهاخ انطثاكح

انتصاق انمعادن انمنصهرج

خالل نماط

عمهاخ انهحاو

انمطاطح وانهذونح

Ductility and plasticity

عمهاخ انتشكم

إزانح انرائش

Chip removal

عمهاخ انتشغم

sand castingانطثاكح انرمهح

انذائمح )تثالهح انطثاكح تانمىانة

Gravity and pressureوضغط(

die casting

انطثاكح تاضتخذاو انطرد انمركسي

Centrifugal casting

Gas weldingنحاو انغاز

نحاو انمىش انكهرت

Electric arc welding

spot weldingنحاو اننمطح

brazing weldingنحاو انمىنح

soldering weldingنحاو انمصذر

forgingانحذادج

rollingانذرفهح

extrusionانثثك

drawingانطحة

pressingانكثص

fittingانثرادج

machiningانخراطح

millingانتفرس

planingانكشط

drillingانتثمة

grindingانتجهخ

( طرق انتصنع انمختهفح وارتثاطها تخىاص انمىاد0.0شكم )


0.2.0Tension Test

i

ii

iii

F

1.11.1

0:

(Modulus of Elasticity or Young Modulus)

i.e.

E =i.e.

stress


straini.e.

0Yield Stress

1Ultimate Stress

2Resilience

2

1


)ب( صهة طري أو لصف صهة ناشف)أ(

0.0

)د( صهة طري أو لصف صهة ناشف)ج(

0 1


3

0.2.0Impact Test

recess

1 1

Hh

w

k

2/)(

cmkgA

hHwk

A

Brittleness

0.1 – 0.2 kg/cm

112

kg/cm


0 2Charpy impact test

1111

0.2.1Hardness Test

0Brinell Hardness Test

√ Brinell hardness number)

kg

mm

mm

0Rockwell Hardness Test

111


11160 kg 10 kg RHA

2.5mm100 kg 10 kg RHB

111150 kg 10 kg RHC

0.2.2Vickers Hardness Test

116

5 kg 140kg

11

0.3Metals Preparation Methods

0.3.0


ferrous metals

(steel

(cast-iron)1

61

0.3.0Iron Ore

1.1

mining

industries metallurgical processes

hematitemagnetite

0.3.1

i.e.


ISemi-Finished Products

0Raw Metal

Molten Metal

Pigs

0Prepared Metal


( Cupola furnace)

1(Castings)

2Forming Lugs

plastic forming

hammering100 kg

3Semi-Rolled Lugs

initial rolling

4

5Square Block

160 cm

6( Rods)


(rolling)extrusion(drawing)

7(Forgings)

02Structural Sections

TI(angleL(channel)∪

00Wire

drawing i.e.

2mm

00Sheet Metals

2mm

bolts

(springs)

press work

metal cutting

i.e.


IIFinished Products

0.3.2Plastic Forming of Metals

0Metal Rolling

beams

anglesi.e.

0Rolling Machines

1 1

gear box

alloy steel


0 3

1Calculation of Angle of Contact

1 6

∝angle of contact

d

tt

d

tt

211

21

1cos

1cos

d

t

t


0 4

0 5

2


N

FNF1.3

N

F

S

Q

S= N cos∝ + F sin∝

Q = F cos∝

1P = N sin∝

QP

)4(22

PQ

PQ

P , Q11

)5(sincos NF


F

)6(NF

𝛍

μ∅

)7(tan

163

)8(tantan

sincostan

sincos

sincos

NN

NN

NF

∝∅

angle of friction

angle of contact1121111

11

3Types of Rolling Machines


Primary Reduction Mills

Structural Sections Mills

beams

rodsangles

Finishing Mills

sheets.

iTwo High Rolls

iiReversing Rolls

1 2

0 6


iiiThree High Rolls

1 9

0 7

iv(Four High Rolls)

) ( forming rolls

(supporting rolls)

1 11


0 02

vMulti High Rolls

10mm

30mm

viUniversal Rolling Mills

1000mm

4Cold Rolling Processes

1

1


1

(internal stresses)

i.e.

5(Hot Rolling Processes)


Chip Generation

0.0(Introduction)

elastic deformationpermanent plastic deformation

i.e.

1.1(mild steel)

i A(Limit of Proportionality)

Hook's law

ii BElastic Limit

iii Ci.e.Yield

Point

iv D

Maximum or Ultimate Stress Point


v EFracture Point

0.0

slip planes

0.0(Types of Chips)

0.0.0Discontinuous Chips


0.0.0Continuous Chips

60m/min

1

1

1

1

1

i

ii

iii

6

0.0.1 (Inhomogeneous Chips or Heterogeneous Chips)

∅

1

1


0.0.2(Fractured Chips)

cracks

0.1

Martensitic Structure

Tool face

0 0


0.2(Forming Operations without Chip Formation)

0.2.0Press Work

punch and die

(The First Type)

Piercing

Blanking

(The Second Type)

Bending

Deep Drawing

0(Shear Processes)

(Piercing and Blanking)


i.e.

1 11 1

1 1

0 10 2


0 3

0(Forming Processes)

i(Bending)

ii(Deep Drawing)

1 6


iii(Stamping Processes)

0 4


Materials Testing and Experimental Methods

1Tensile Tests

ductile materialmild steel

i.e.

i.e.

i.e.

1The Working Portion of the Specimen

wedge

i.e.0.01d


1Testing Machines

in the elastic range(extensometer)

(strain gauge)

(pair of dividers and graduated rule)

1Effect of Rate of Loading

hardened steel

1

(Variation of Elongation with Gauge Length and Cross – Sectional Area )

1


1

el

e = a + bl

= 100e/l = 100a/l + 100b

Unwina

AC √A100a100b=B

Bl

AC

l

e100


B CB=20 C =70

B. S. 18

Al 4

1Overstrain and Repeated Loading

i.e.)

Hook's law

1


1

1Proof Stress

1

1


OTPQOTQ

OP = 0.1%Q

OT

1Compression Tests

BucklingLength=minimum

breadth

1(Failure in Brittle Materials)

11

𝛉 ∅

∅

∅

𝛉


𝛉

𝛉

𝛉 ∅

1.1AP

σ𝛉∅

σ P /A

BB = A/ cos θ

PN

(Q)


1.2P


22 cos.cos

cos/

cos

A

P

A

p

B

NN

tancostancos 2

2

A

P

θσr

P


(*)tancoscossin 2 fQr

σr

𝛉

#2/45

902

902

)902tan()290tan(tan

2cot2sin

2cos

cossin2

sincostan

tancossin2sincos

0tancossin2cossin

0)sincos2tan

)cos()cos(cossinsin

22

22

22

2

d

d

zerod

d

r

r


(Strain Energy Methods)

1.0(Internal Strain Energy)

PU

LAE

1

LTU

GJ

2

LMU

I

3


(Positive scalar quantity).

1.6(Sign Conventions)

1.4(Castigliano's Theorem)

1.1

(Application to Statically Determinate Problems)


(fictitious force)

1

(Application to Statically Indeterminate Problems)

1.2(Assumption and Limitations)

(law of Superposition)

1.4 (Solved Examples in Strain Energy)

0

P


(a) (b)

1.0

(4 1 (a) )

ALE

(Linear) ( (b) )P

B

OBA

U


B

P

∫

6

T (torque).

1.6

(4 2 (b) )

BOBA

(a) o

T

𝚯 L

T T A

(b)

𝜽


U

∫

4


4 3 B

OAB

∫

1.4


1.4(Derivation of Castigliano Theorem)

4 4

n123

n

n


1.1

1

34


1.4(Solved Examples in Castigliano Theorem)

1

∫


∫

∫

∫

*

+

5

∫

∫

∫

∫


∫

∫

2

∫

∫

∫

∫

∫

∫


4

∫

∫

∫ (

)

∫


4

∫

∫

∫

∫

(

)

∫

∫ (

)


∫

∫ (

)

4

P

∫

∫

P:

∫

∫


∫

∫

∫

∫

01

9

∫

∫


∫

∫

∫

∫

∫

00

RBA

PA


∫

∫

∫

∫

∫

[

]

60

A11


A

∫

∫

∫

∫ (

)

[

]

40


Q

∫

∫

∫ [

]

∫ [

(

)

]

01


∫

∫

∫

∫

(

)

∫

∫ (

)

∫

∫ [

]

*

+

*

+


1.01(Exercises in Castigliano Theorem)

0

13P

,

(

)-

6

,

-

4


,

-

1

PA

,

-

5

A11

,

-


2

A

,

-

4

ABP

,

-

4

7P

{

}


4

A

,

-

01

{ }

00

P11


{

}

06

{

}

04

RAB

PB

{

}


5.0(Introduction)

5 1

5.0

𝑄𝑃

𝑄𝑃 اإلجهاد إجهاد الخضوع

اإلنفعال


5.6(Method of Determining Critical Load) 8

0Bending Moment Diagram Methods))

0


6

4


6(Virtual Work Method)

i

ii

iii

iv


1

P

(

)


5

2


∫

[

(

)]

A

4


(A)

(

) (

)

4


(

)

(

)

4


B

B

C

123


01


P3P

P

(

)

3P

(

) (

)


5 4

(Exercises in Plastic Collapse of Beams and Simple Frames)

0

{

}

6

{

}


4

{

}

1

{

}

5

{

}


2

{

}

4

{

}

4

{

}


4

{

}

9


(Plastic Theory of Bending)

2.0(Bending Beyond the Yield Stress)

(edge stress)

(mild steel)

i.e.

1121


2.6(Assumptions in the Plastic Theory)

1

2

3

4

2.4(Moment of Resistance at a Plastic Hinge)

(a) )

(b))

(c)


(a)(Rectangular Section) 8

2.0

bd

Z


Si.e.

13

23

12

56

0

72mm 30mm


3

6 1 (b)


(b)I (I – Section)8

(flange)(web)

1 152

6

I


(i)(ii)

(c)(Unsymmetrical Section) 8

6 2

2.6


4

6 3

8


2.4

::::::::::::::::: واهلل انمىفك

أسامة حممد املرضي سليمان

قســه اهليدســة امليكاىيكيــة

كليــة اهليدســة والتقييــة

جامعــة وادي الييــل


1www.jalalalhajabed.com

1

1111

1

The Iraqi Journal for Mechanical and Material Engineering

11119

1111

1991

611

1111

3

1119

2

1113

91113

111922

http://www.jalalalhajabed.com/


11

1931

11111

1991

11

1111

11111

1111

Mikell P Groover, "Fundamentals of Modern Manufacturing”, John Wiley and

Sons Inc., (2007).

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th

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, th

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American Machinist, McGraw Hill, New York, (1979).

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edition, Butterworth Company, London, (1984).

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edition, PWS –

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Wiley, Hoboken, N. J., (2000).

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McGraw Hill, August 12 (2010).


ىبـــذة عـ املــــؤلف

1966

1991

1998

2113

Documents

ةىودـللاو ةىورـلما تايـساسأ باتـك€¦ · Author Osama Mohammed Elmardi Suleiman Assistant Professor, Faculty of Engineering, Nile Valley University